# Effect of Ball Burnishing Pressure on Surface Roughness by Low Plasticity Burnishing Inconel 718 Pre-Turned Surface

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Modeling of Low Plasticity Burnished Surface Roughness

#### 2.1. Surface Formation Mechanism of LPB

_{lim}). It signified that the surface roughness reached the minimum value. The surface roughness was stable at the minimum value until the pressure exceeded the transforming pressure (P

_{t}), which connotes the end of SS. Therefore, the optimal LPB pressure interval was [P

_{lim}, P

_{t}], as shown in Figure 4.

_{t}. The surface material could be extruded out and piled up near the indentation. The surface roughness was only deteriorated by the pile-up when the pressure was less than the deep indentation pressure (P

_{d}). The surface roughness was deteriorated by the combined effects of the indentation and pile-up when the pressure is higher than P

_{d}.

_{y}which could accurately reflect the surface roughness was employed for the surface roughness assessment. Several assumptions of the prediction model were summarized as follows:

- (a)
- The turned surface roughness peaks are simplified to wedge shapes.
- (b)
- The roller is simplified as a line since the diameter of the roller is much larger than the surface roughness peak.
- (c)
- The plastic deformation of the surface wedge is larger compared to that of the elastic deformation. Therefore, the material of the surface roughness peak is assumed as the ideal rigid-plastic material and the roller rigid body.
- (d)
- The frictional coefficient between the ball and the workpiece is 10
^{−5}~5 × 10^{−3}[24]. Therefore, the surface is assumed to be frictionless to simplify the model derivation. - (e)
- The surface is flat when the surface roughness reaches the minimum value.
- (f)
- The low boundary of surface roughness is not affected by the pile-up.

#### 2.2. Modeling of Surface Roughness in SS

_{y}

_{0}) and the half-width of the wedge (l) could be measured from the tool marks. P is the LPB pressure. The press depth (c) and the half-width of the contact area (h) could be expressed as Equation (1). The slip-line angle (ψ) could be calculated by Equation (2) [22,25].

_{s}is the yield strength of workpiece material. The rolling force F can be calculated by Equation (4) for the LPB process [26].

_{y0}is the initial surface roughness.

_{lim}) corresponding to the minimum surface roughness could be expressed as Equation (6).

_{s}) and the radius of the roller (R

_{ball}) are the constants of the workpiece and the roller. The only input variable is the LPB pressure (P).

#### 2.3. Modeling of Surface Roughness in IS

_{t}. That was because the residual indentation occurred under the excessive LPB pressures. The extruded material piled up surrounding the indentation, and the surface roughness was aggravated. The slip-line field theory was used to calculate the height of the pile-up. By superimposing it with the R

_{lim}, the surface roughness of the IS could be finally obtained [25].

_{r}) remained on the surface. The material surrounding the indentation was higher than the initial surface [28]. The pile-up was only related to the residual indentation. Therefore, δ

_{r}needs to be calculated first, which is shown in Equation (8).

_{1}, and R

_{2}are the radius of the rolling ball and the workpiece to be machined, respectively. E

_{1}, E

_{2}, ν

_{1}, ν

_{2}are the elastic modulus and Poisson’s ratio of the roller and the workpiece material, respectively [29].

_{Y}and δ

_{Y}shown in Equation (11) are the critical load and displacement corresponding to the beginning of the surface plastic deformation, which could be calculated with Equations (12) and (13), respectively. P

_{0Y}is the maximum contact stress when the surface material yields. P

_{0Y}= 1.6σ

_{s}for the von Mises yielding criterion [29].

_{r}could be calculated with Equations (8) to (13). The surface formation stage went into SS when δ

_{r}> 0. The transforming pressure (P

_{t}) corresponding to the beginning of the SS could be expressed as Equation (14) by substituting δ′ = δ into Equation (11).

_{t}. Therefore, the optimal interval of the LPB pressure could be expressed as [P

_{lim}, P

_{t}].

_{r}was the residual displacement calculated above. According to the geometrical considerations, the width of residual indentation (a

_{2}) could be expressed as Equation (15).

_{2}) could be obtained with Equation (16).

_{2}and the slip-line angle (ψ

_{2}) is shown in Equation (17).

_{2}) could be calculated with Equation (18).

_{2}) could be expressed in Equation (19).

_{2}) could be obtained by Equation (20).

_{y}) was only affected by e

_{2}when δ

_{r}≤ R

_{y}

_{,lim}. When δ

_{r}> R

_{y}

_{,lim}, the residual indentation depth was lower than the original boundary, and the surface roughness was affected by both δ

_{r}and e

_{2}. The R

_{y}could be expressed as Equation (21).

#### 2.4. Validation of Proposed Model Prediction Results

_{OP}) and the error of it (E

_{I}), error of the minimum surface roughness (E

_{Rmin}) and surface roughness at 10.4 MPa (E

_{R10.4}) were employed to evaluate the accuracy of the model. The experimental results and the predicted results were shown in Figure 8.

_{Rmin}was 15.5%. However, the predicted value at 10.9 MPa was still 2.104 μm with the E

_{R}

_{10.4}of 30.1%. The predicted I

_{op}was [4.8 MPa, +∞) with the error E

_{I}= +∞, which was apparently incorrect. The predicted results indicated that the model of Li cannot accurately predict the surface roughness and optimize the LPB pressure. This is due to the pile-up under higher LPB pressures not being considered in the model of Li.

_{Rmin}was 0.8%. The predicted result at 10.9 MPa was 3.413 μm, and the E

_{R}

_{10.4}was 13.3%. The predicted I

_{op}was 4.8 MPa, and the E

_{I}was 25%. The proposed model could predict the surface roughness accurately compared with the model of Li, and it could be used to optimize the LPB pressure. The difference between the experiment and prediction results is due to the measurement error in the geometric parameters of tool marks. The random error of roughness peak geometric parameters could be reduced by measuring more surface roughness peaks. By means of that, the prediction accuracy of the proposed model could be improved.

## 3. Experiments

#### 3.1. Materials

#### 3.2. Experimental Method

_{p}= 0.1 mm. The size of the specimen was ϕ24 × 140 mm. Four rolled sections were set for each specimen to be processed with different rolling parameters.

_{y}was selected as the surface roughness assessment index. To ensure reliability, R

_{y}for each group was measured three times and their average value was taken as the final value.

## 4. Results and Discussion

#### 4.1. Experimental Results

_{y}was measured to be 4.179 μm (standard deviation 0.037 μm). The periodically distributed tool marks were observed on a turned surface. The wedge shape of the tool marks supported the simplification of the model.

#### 4.2. Surface Roughness Prediction and the LPB Pressure Optimization for LPBed Inconel 718

_{OP}), the maximum error (E

_{max}), the error of the minimum roughness (E

_{Rmin}) and the surface roughness at 21 MPa (E

_{R,}

_{21}) were used to evaluate the model.

_{y,min}) calculated by the model was 1.031 μm with an error E

_{Rmin}4.4%. The experimental surface roughness at 21 MPa was 1.217 μm. The predicted surface roughness under 21 MPa was 1.263 μm. The error E

_{R,21}was only 3.8%, which was much lower than the error of Li’s model (15.3%). The above evaluation proved that the proposed model could be used to predict surface roughness with high accuracy even under excessive pressures.

## 5. Conclusions

- (1)
- The analytical prediction model for the LPBed surface roughness was proposed based on Hertz contact mechanics and slip-line field theory. The increment of the surface roughness in IS was attributed to the pile-up. Considering the deterioration, the proposed model could successfully predict surface roughness under excessive pressures.
- (2)
- The LPBed surface roughness of AISI 1042 was used to validate the proposed model. The predicted result of the minimum roughness was 2.512 μm (the error was 0.8%). Moreover, the surface roughness at 10.4 MPa was 3.413 μm (13.3%). According to the proposed model, the optimal LPB pressure corresponding to the minimum surface roughness was 4.8 MPa (25%). The results of Li’s model were 2.104 μm (15.5%), 2.104 μm (30.1%) and [4.8 MPa, +∞) (+∞%), respectively. Considering the pile-up, the proposed model could predict the surface roughness and the optimal pressures more accurately compared with the model of Li.
- (3)
- The Inconel 718 was manufactured under different LPB pressures. The tool marks could be smoothed out by the LPB process. The minimum value of surface roughness was 1.079 μm. The surface roughness decreased by 72.9% compared with the turned surface roughness. However, the minimum surface roughness was limited. The surface roughness increased by 12.8% when the pressure reached 21 MPa. Pile-up and indentations observed under excessive pressures supported the deterioration of the surface roughness.
- (4)
- The proposed model was used to predict the surface roughness and the optimal interval of the LPB pressure. The error in the proposed results was less than 7%. The proposed model was more accurate than Li’s model (15.3%). The predicted optimal interval (12.2 MPa to 17.5 MPa) was consistent with the experimental one (12 MPa to 18 MPa). The proposed model could be used to predict the LPBed surface roughness of Inconel 718, and further conduct the LPB process.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Simulated LPB surface profile with pile-up obtained. (Reprinted with permission from Ref. [16]; published by Elsevier, 2013).

**Figure 9.**Experimental steps. (

**a**) Turning and LPB process and equipment; (

**b**) Processing details and the machining coordinate system establishment; (

**c**) The specimens after turning and LPB process; (

**d**) Surface topography instruments and measurement process.

**Figure 10.**Surface topography of machined Inconel 718. (

**a**) Turned, (

**b**–

**d**) LPBed under different pressures of 9 MPa, 15 MPa, 21 MPa, respectively.

**Figure 11.**Surface roughness peak simplification and geometric parameters measurement. (The blue line is the measured surface roughness peak. The red line is the simplified wedge. The red dot line indicate the wedge angle).

Material | E (GPa) | ν | σ_{s} (MPa) | σ_{b} (MPa) | R_{y0} (μm) | α (°) | R_{ball} (mm) |
---|---|---|---|---|---|---|---|

AISI 1042 | 210 | 0.3 | 300 | 570 | 6.3 | 170.8 | 9 |

Material | E (GPa) | ν | σ_{s} (MPa) | σ_{b} (MPa) |
---|---|---|---|---|

Inconel 718 | 205 | 0.3 | 1360.5 | 1502 |

SiN (Roller) | 300 | 0.27 | - | - |

Results | R_{y,min} (μm) | E_{Rmin} | R_{y,}_{21} (μm) | E_{R}_{21} | E_{max} | I_{OP} (MPa) |
---|---|---|---|---|---|---|

Prediction | 1.031 | 4.4% | 1.263 | 3.8% | 7.0% | [12.2, 17.5] |

Experiment | 1.079 | - | 1.217 | - | [12, 18] |

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**MDPI and ACS Style**

Cui, P.; Liu, Z.; Yao, X.; Cai, Y. Effect of Ball Burnishing Pressure on Surface Roughness by Low Plasticity Burnishing Inconel 718 Pre-Turned Surface. *Materials* **2022**, *15*, 8067.
https://doi.org/10.3390/ma15228067

**AMA Style**

Cui P, Liu Z, Yao X, Cai Y. Effect of Ball Burnishing Pressure on Surface Roughness by Low Plasticity Burnishing Inconel 718 Pre-Turned Surface. *Materials*. 2022; 15(22):8067.
https://doi.org/10.3390/ma15228067

**Chicago/Turabian Style**

Cui, Pengcheng, Zhanqiang Liu, Xinglin Yao, and Yukui Cai. 2022. "Effect of Ball Burnishing Pressure on Surface Roughness by Low Plasticity Burnishing Inconel 718 Pre-Turned Surface" *Materials* 15, no. 22: 8067.
https://doi.org/10.3390/ma15228067