# Influence of Ball-Burnishing Process on Surface Topography Parameters and Tribological Properties of Hardened Steel

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Surface smoothing (geometrical) mechanism,
- Surface enhancement (mechanical) mechanism,
- The microstructural (metallurgical [11]) mechanism.

## 2. Materials and Methods

^{2}. Measured textures were only levelled without digital filtration. Then, surface topography parameters were calculated using the TalyMap software. Investigations were conducted based on Hartley’s static, determined plan. Such a plan can be built on a hypercube or hypersphere. In this work, a hypercube was used. In the case of a three-level plan, Hartley’s plan makes it possible to determine the regression function in the form of a polynomial of the second degree. Its general form is presented in Formula (1):

- x
_{1}—burnishing pressure force: 10, 20, and 30 MPa, - x
_{2}—burnishing speed: 400, 700, and 1000 mm/min, - x
_{3}—stepover: 30, 50, and 70 µm:

_{max}(${\overline{y}}_{i3}$) were taken as the result factors. Other surface topography parameters were also measured and compared to the values achieved after the grinding process (see Table 3).

^{0}apart) perpendicular to the wear track in order to obtain the cross-sectional area of the wear tracks. Then, the values of the cross-sectional area of the wear track (in TalyMap software defined as the area of the hole) were averaged and the value of volumetric wear was calculated using Formula (2):

- d—diameter of the wear track (in our tests d = 10 mm),
- S—area of the hole (the cross-sectional area of the wear track).

## 3. Results and Discussion

#### 3.1. Effect of the Ball-Burnishing Parameters on the Surface Topography and Residual Stresses

_{max}are presented in Table 2. Table 3 shows the ranges of all measured surface topography parameters obtained through the ball-burnishing process. A comparison to the parameters obtained after the grinding process was also presented in Table 3. Figure 3 presents isometric views of the selected samples after ball burnishing with the highest and the lowest value of the Sq parameter as well as the Abbott–Firestone curve and distribution of surface ordinates.

_{max}for the ground surface was 96 MPa (tensile stress). After ball burnishing, σ

_{max}achieved values in the range of −283 ÷ −493 MPa (compressive stresses). The largest value of the compressive stresses was calculated for the sample from variant 2, where the burnishing pressure force equaled 30 MPa, the burnishing speed 400 mm/min, and stepover was set to 30 µm.

#### 3.2. Effect of the Ball-Burnishing Parameters on the Tribological Properties

- The mean value of the volumetric wear of the disc samples (VD),
- The sliding distance after which the friction force obtains steady-state conditions (DSS),
- The average value of the friction force after obtaining the steady-state condition (Fav).

_{s}= 0.16 m/s.

^{3}). On the other hand, the largest wear volume (0.219 mm

^{3}) was observed when the DSS parameter was the smallest (22 m).

_{s}= 0.48 m/s. At the sliding speed of 0.32 m/s, the largest value of wear volume was calculated for sample 2 (0.162 mm

^{3}). For this sample, DSS parameter was the largest (70 m) and Fav was the smallest (4.78 N). The maximum wear volume was observed in the case of sample 3. The value of VD reached 0.231 mm

^{3}.

_{s}=0.48 m/s, the smallest value of wear volume was also observed for sample 2. In this case, the value of the VD parameter reached 0.171 mm

^{3}and, like at lower sliding speeds, corresponded to largest value of the DSS parameter (62 m). The average value of the friction force after obtaining the steady-state condition Fav was also the smallest but identical to the sample 11 (4.62 N). The highest value of wear volume was characterized by sample 3 and it was 0.245 mm

^{3}. In this case, the distance to obtain steady-state conditions of the friction force DSS reached the value of 19 m, but shorter distance was observed for sample 6 (15 m).

_{s}= 0.16 m/s, the average value of the coefficient of friction ranged between 0.478 (sample 2) and 0.565 (sample 3) during dry sliding tests; at v

_{s}= 0.32 m/s, it was between 0.478 (sample 2) and 0.546 (sample 3); and at a highest sliding speed, the value of the friction coefficient reached 0.501 (for sample 2) and 0.559 (for sample 6).

_{s}= 0.32 m/s) to −0.83 (v

_{s}= 0.48 m/s). Linear relationships were also observed in the case of wear volume and several surface topography parameters, like Sz, Sdq, Spc, Sk, and Svk. The correlation coefficient oscillated between 0.69 and 0.86.

_{max}(Figure 9). It was an inversely proportional relationship and the correlation coefficient reached the values up to −0.9. A similar value was observed between wear volume and the sliding distance DSS.

## 4. Conclusions

_{max}was correlated with wear volume.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Scheme of the Computer Numerical Control (CNC) test stand (

**a**) and photo of working chamber (

**b**).

**Figure 3.**Isometric views (

**a**,

**b**) and Abbott–Firestone curves with distribution of surface ordinates (

**c**,

**d**) for the samples with the lowest (

**a**,

**c**) and the highest (

**b**,

**d**) value of the Sq parameter.

**Figure 4.**Dependence between ball-burnishing parameters (P, v) and surface topography parameters Sq (

**a**), Sz (

**b**).

**Figure 5.**Dependence between ball-burnishing parameters (P, a) and surface topography parameters Sq (

**a**), Sz (

**b**).

**Figure 6.**Dependence between ball-burnishing parameters (v, a) and surface topography parameters Sq (

**a**), Sz (

**b**).

**Figure 8.**Dependency between disc volumetric wear VD and skewness Ssk at the sliding speed of: (

**a**) 0.16 m/s; (

**b**) 0.48 m/s.

**Figure 9.**Dependency between disc volumetric wear VD and maximum value of stresses in the surface layer σ

_{max}at the sliding speed of: (

**a**) 0.16 m/s; (

**b**) 0.48 m/s.

Central Values of the Entry Factors | Units of Variation | Encoded Input Factors |
---|---|---|

${\widehat{\mathrm{x}}}_{10}=\frac{{\mathrm{P}}_{\mathrm{max}}+{\mathrm{P}}_{\mathrm{min}}}{2}=20$ | $\Delta {\widehat{\mathrm{x}}}_{1}=\frac{{\mathrm{P}}_{\mathrm{max}}-{\mathrm{P}}_{\mathrm{min}}}{2}=10$ | ${\mathrm{x}}_{1}=\frac{\mathrm{P}-{\widehat{\mathrm{x}}}_{10}}{\Delta {\widehat{\mathrm{x}}}_{1}}=\frac{\mathrm{P}-20}{10}$ |

${\widehat{\mathrm{x}}}_{20}=\frac{{\mathrm{v}}_{\mathrm{max}}+{\mathrm{v}}_{\mathrm{min}}}{2}=700$ | $\Delta {\widehat{\mathrm{x}}}_{2}=\frac{{\mathrm{v}}_{\mathrm{max}}-{\mathrm{v}}_{\mathrm{min}}}{2}=300$ | ${\mathrm{x}}_{2}=\frac{\mathrm{v}-{\widehat{\mathrm{x}}}_{20}}{\Delta {\widehat{\mathrm{x}}}_{2}}=\frac{\mathrm{v}-700}{300}$ |

${\widehat{\mathrm{x}}}_{30}=\frac{{\mathrm{a}}_{\mathrm{max}}-{\mathrm{a}}_{\mathrm{min}}}{2}=50$ | $\Delta {\widehat{\mathrm{x}}}_{3}=\frac{{\mathrm{a}}_{\mathrm{max}}-{\mathrm{a}}_{\mathrm{min}}}{2}=20$ | ${\mathrm{x}}_{3}=\frac{\mathrm{a}-{\widehat{\mathrm{x}}}_{30}}{\Delta {\widehat{\mathrm{x}}}_{3}}=\frac{\mathrm{a}-50}{20}$ |

_{max}, P

_{min}—maximum and minimum value of burnishing pressure force; v

_{max}, v

_{min}—maximum and minimum value of burnishing speed; a

_{max}, a

_{min}—maximum and minimum value of stepover.

No | ${\mathit{x}}_{1}$ | ${\mathit{x}}_{2}$ | ${\mathit{x}}_{3}$ | ${\mathit{x}}_{1}^{2}$ | ${\mathit{x}}_{2}^{2}$ | ${\mathit{x}}_{3}^{2}$ | ${\mathit{x}}_{1}{\mathit{x}}_{2}$ | ${\mathit{x}}_{1}{\mathit{x}}_{3}$ | ${\mathit{x}}_{2}{\mathit{x}}_{3}$ | ${\overline{\mathit{y}}}_{\mathit{i}1}\left(\mathit{S}\mathit{q}\right),\mu \mathbf{m}$ | ${\overline{\mathit{y}}}_{\mathit{i}2}\left(\mathit{S}\mathit{z}\right),\mu \mathbf{m}$ | ${\overline{\mathit{y}}}_{\mathit{i}3}\left({\mathsf{\sigma}}_{\mathbf{max}}\right),\mathit{M}\mathit{P}\mathit{a}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | + | + | + | + | + | + | + | − | − | 0.0835 | 1.19 | −401 |

2 | + | − | − | + | + | + | − | − | + | 0.0685 | 0.85 | −493 |

3 | − | + | − | + | + | + | − | + | − | 0.141 | 1.47 | −282 |

4 | − | − | + | + | + | + | + | + | + | 0.169 | 1.65 | −361 |

5 | + | 0 | 0 | + | 0 | 0 | 0 | 0 | 0 | 0.051 | 0.558 | −466 |

6 | − | 0 | 0 | + | 0 | 0 | 0 | 0 | 0 | 0.153 | 1.79 | −308 |

7 | 0 | + | 0 | 0 | + | 0 | 0 | 0 | 0 | 0.149 | 1.07 | −338 |

8 | 0 | − | 0 | 0 | + | 0 | 0 | 0 | 0 | 0.162 | 1.11 | −457 |

9 | 0 | 0 | + | 0 | 0 | + | 0 | 0 | 0 | 0.194 | 1.46 | −397 |

10 | 0 | 0 | − | 0 | 0 | + | 0 | 0 | 0 | 0.175 | 1.17 | −382 |

11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.133 | 1.19 | −359 |

Surface Topography Parameters [29] | Workpiece | ||||
---|---|---|---|---|---|

Ground | Burnished | ||||

Min. | Max. | ||||

Height | Root mean square height | Sq [µm] | 0.522 | 0.051 | 0.194 |

Skewness | Ssk | −0.431 | −0.345 | 0.244 | |

Kurtosis | Sku | 3.78 | 1.99 | 3.26 | |

Maximum peak height | Sp [µm] | 2.37 | 0.294 | 0.805 | |

Maximum pit height | Sv [µm] | 5.92 | 0.264 | 1.03 | |

Maximum height | Sz [µm] | 8.29 | 0.558 | 1.79 | |

Arithmetic mean height | Sa [µm] | 0.412 | 0.041 | 0.339 | |

Functional | Areal material ratio | Smr [%] | 0.162 | 93.5 | 100 |

Inverse areal material ratio | Smc [µm] | 0.639 | 0.0647 | 0.266 | |

Extreme peak height | Sxp [µm] | 1.15 | 0.0969 | 0.339 | |

Spatial | Auto-correlation length | Sal [mm] | 0.188 | 0.0358 | 0.217 |

Texture-aspect ratio | Str | 0.383 | 0.0237 | 0.245 | |

Texture direction | Std [^{o}] | 73.3 | 0.623 | 7.1 | |

Hybrid | Root mean square gradient | Sdq | 0.101 | 0.00613 | 0.0234 |

Developed interfacial area ratio | Sdr [%] | 0.499 | 0.00188 | 0.0273 | |

Functional | Material volume | Vm [mm^{3}/mm^{2}] | 2.01 × 10^{−5} | 2.53 × 10^{−6} | 6.90 × 10^{−6} |

(volume) | Void volume | Vv [mm^{3}/mm^{2}] | 0.000659 | 6.72 × 10^{−5} | 2.73 × 10^{−4} |

Peak material volume | Vmp [mm^{3}/mm^{2}] | 2.01 × 10^{−5} | 2.53 × 10^{−6} | 6.90 × 10^{−6} | |

Core material volume | Vmc [mm^{3}/mm^{2}] | 0.000466 | 4.47 × 10^{−5} | 1.88 × 10^{−4} | |

Core void volume | Vvc [mm^{3}/mm^{2}] | 0.00059 | 6.16 × 10^{−5} | 2.55 × 10^{−4} | |

Pit void volume | Vvv [mm^{3}/mm^{2}] | 6.93 × 10^{−5} | 5.61 × 10^{−6} | 2.08 × 10^{−5} | |

Feature | Density of peaks | Spd [1/mm^{2}] | 502 | 243 | 448 |

Arithmetic mean peak curvature | Spc [1/mm] | 81.8 | 6.05 | 15.5 | |

Ten-point height | S10z [µm] | 3.77 | 0.325 | 1.08 | |

Five-point peak height | S5p [µm] | 1.42 | 0.188 | 0.489 | |

Five-point pit height | S5v [µm] | 2.35 | 0.136 | 0.591 | |

Mean dale area | Sda [mm^{2}] | 0.0019 | 0.00151 | 0.00447 | |

Mean hill area | Sha [mm^{2}] | 0.00195 | 0.00181 | 0.00372 | |

Mean dale volume | Sdv [mm^{3}] | 7.06 × 10^{−8} | 1.16 × 10^{−8} | 2.62 × 10^{−8} | |

Mean hill volume | Shv [mm^{3}] | 7.85 × 10^{−8} | 1.19 × 10^{−8} | 2.14 × 10^{−8} | |

Functional | Core roughness depth | Sk [µm] | 1.04 | 0.106 | 0.421 |

(stratified | Reduced summit height | Spk [µm] | 0.358 | 0.0433 | 0.0853 |

surfaces) | Reduced valley depth | Svk [µm] | 0.557 | 0.0407 | 0.162 |

Upper bearing area | Smr1 [%] | 8.68 | 3.66 | 11.4 | |

Lower bearing area | Smr2 [%] | 87.8 | 90.2 | 95.2 |

**Table 4.**Results of the tribological tests. VD: Mean value of the volumetric wear of the disc samples. DSS: Sliding distance after which the friction force obtains steady-state conditions. Fav: Average value of the friction force after obtaining the steady-state condition.

No | v_{s} = 0.16, m/s | v_{s} = 0.32, m/s | v_{s} = 0.48, m/s | ||||||
---|---|---|---|---|---|---|---|---|---|

VD, mm^{3} | DSS, m | Fav, N | VD, mm^{3} | DSS, m | Fav, N | VD, mm^{3} | DSS, m | Fav, N | |

1 | 0.166 | 68 | 5.44 | 0.171 | 62 | 4.87 | 0.191 | 54 | 5.42 |

2 | 0.147 | 81 | 4.69 | 0.162 | 70 | 4.78 | 0.171 | 62 | 4.92 |

3 | 0.219 | 22 | 5.54 | 0.231 | 18 | 5.36 | 0.245 | 19 | 5.48 |

4 | 0.205 | 64 | 5.26 | 0.193 | 40 | 4.92 | 0.233 | 28 | 5.37 |

5 | 0.159 | 71 | 5.19 | 0.174 | 44 | 4.81 | 0.186 | 37 | 4.98 |

6 | 0.208 | 65 | 4.89 | 0.222 | 25 | 5.09 | 0.249 | 15 | 5.49 |

7 | 0.188 | 33 | 4.95 | 0.197 | 34 | 5.18 | 0.213 | 46 | 5.14 |

8 | 0.178 | 59 | 5.11 | 0.183 | 64 | 5.33 | 0.177 | 37 | 4.98 |

9 | 0.191 | 38 | 5.37 | 0.188 | 51 | 4.97 | 0.206 | 55 | 5.23 |

10 | 0.198 | 52 | 4.91 | 0.214 | 30 | 5.22 | 0.221 | 49 | 5.31 |

11 | 0.189 | 55 | 5.04 | 0.204 | 38 | 5.02 | 0.198 | 61 | 4.92 |

Ground | 0.278 | 79 | 5.71 | 0.285 | 72 | 5.45 | 0.309 | 68 | 5.77 |

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**MDPI and ACS Style**

Dzierwa, A.; Markopoulos, A.P.
Influence of Ball-Burnishing Process on Surface Topography Parameters and Tribological Properties of Hardened Steel. *Machines* **2019**, *7*, 11.
https://doi.org/10.3390/machines7010011

**AMA Style**

Dzierwa A, Markopoulos AP.
Influence of Ball-Burnishing Process on Surface Topography Parameters and Tribological Properties of Hardened Steel. *Machines*. 2019; 7(1):11.
https://doi.org/10.3390/machines7010011

**Chicago/Turabian Style**

Dzierwa, Andrzej, and Angelos P. Markopoulos.
2019. "Influence of Ball-Burnishing Process on Surface Topography Parameters and Tribological Properties of Hardened Steel" *Machines* 7, no. 1: 11.
https://doi.org/10.3390/machines7010011