# Asymmetric Height Distribution of Surfaces Machined by Hard Turning and Grinding

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Material

#### 2.2. Machining and Experimental Plan

#### 2.3. Measurement and Texture Parameters

_{c}= 0.8 mm cut-off and Gauss filter were applied. For the analysis of the parameters, the standard ISO 25178 was used. The evaluation area was 2 mm × 2 mm, so the number of the obtained topography points was 1 million. One area per surface was scanned; the measurement was not repeated because of the great amount of the obtained surface points (the 3D area is equivalent to 1000 2D profiles) and the consistence of the surface around the circumference of it.

## 3. Results and Discussion

_{p}) values separately. The numerical values of Ssk are summarized in Table A1 and Table A2. The negative skewness values are favorable from a tribological (lubricant retention ability and wear resistance) point of view. Earlier studies can be confirmed by the measurement results [30,43]. For a

_{p}= 0.05 mm, the negative values vary between −0.31 and −0.03; for a

_{p}= 0.1 mm, between −0.52 and −0.04; for a

_{p}= 0.2 mm, between −0.38 and−0.16; and for a

_{p}= 0.3 mm, between −0.24 and −0.07. In all four cases, the negative values are found at 0.05 mm/rev and 0.1 mm/rev feed rates. When higher feed rates were applied, only positive skewness values were obtained. However, positive values also appeared within the lower range of the feed rate. By increasing the feed rate, the skewness values show a clear increase only in the case of the highest depth-of-cut (Figure 6b). The cutting speed and the depth-of cut do not influence the skewness values. The reason for the negative values for the lower feed rates is almost certainly that the corner radius of the insert (0.8 mm) is significantly (8 or 16 times) higher than the feed rate and, therefore, the burnishing effect of the insert results in more filled surfaces.

_{p}= 0.1 mm depth-of-cut and 120 m/min cutting speed. Their feed rates were 0.05 mm/rev (S25) and 0.2 mm/rev (S28). The skewness of the former is −0.52 and the latter is 0.959. In Figure 8, it can be observed that the surface machined by a 0.05 mm/rev feed rate is more filled than the other. The Vmp and the Vvv values are also demonstrated in Figure 8. The Vmp value of the higher-skewness surface is five times higher, which is related to the peaky feature of the surface. The 21% lower value of the Vvv of this surface means that the volume of the valleys is higher; therefore, the capillary effect is less remarkable. The filled or plateau-like surface can also be recognized by the slope of the middle part (between 10 and 80%) of the Abbott–Firestone curve. The relatively lower slope in the case of S25 (lower feed rate) means a more filled surface.

## 4. Conclusions

- The asymmetric height distribution of machined surfaces with negative skewness value (Ssk) is favorable from a tribological point of view. In hard turning, a negative value was obtained for Ssk only when the machining was carried out at 0.05 or 0.1 mm/rev feed rate. The Ssk values are not influenced by the depth-of-cut and the cutting speed.
- No similar connection was observed in the case of grinding. The Ssk values are not influenced by the considered technological parameters (infeed velocity and revolutions per minute of the workpiece).
- According to earlier studies, the Ssk parameter is sensitive to sporadic peaks and relatively deep valleys. This was confirmed by the result obtained in grinding and in hard turning at higher feed rates (f > 0.1 mm/rev).
- Medium-strength relationships were obtained for the connection between Ssk and the volume parameters Vmp and Vvv based on the coefficient of correlation (based on linear connection) and the coefficient of determination (based on quadratic connection).
- Low Vmp and Vvv values were found for hard-turned surfaces with negative Ssk values. The deviation of these Ssk values is relatively low. The Ssk values show no trend and they are among the minimum Vmp or Vvv values.

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**The measured Ssk [−], Vmp [ml/m

^{2}] and Vvv [ml/m

^{2}] values of the hard-turned surfaces.

v_{c} [m/min] | f [mm/rev] | a_{p} = 0.05 mm | a_{p} = 0.1 mm | a_{p} = 0.2 mm | a_{p} = 0.3 mm | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Ssk | Vmp | Vvv | Ssk | Vmp | Vvv | Ssk | Vmp | Vvv | Ssk | Vmp | Vvv | ||

60 | 0.05 | −0.031 | 0.007 | 0.018 | −0.425 | 0.007 | 0.021 | 0.043 | 0.007 | 0.017 | 0.051 | 0.009 | 0.028 |

0.1 | 0.487 | 0.009 | 0.019 | 0.194 | 0.011 | 0.022 | −0.158 | 0.008 | 0.022 | 0.300 | 0.010 | 0.025 | |

0.15 | 0.643 | 0.017 | 0.026 | 0.578 | 0.020 | 0.030 | 0.436 | 0.025 | 0.039 | 0.523 | 0.019 | 0.026 | |

0.2 | 0.652 | 0.048 | 0.035 | 0.517 | 0.020 | 0.037 | 0.422 | 0.042 | 0.047 | 0.537 | 0.046 | 0.035 | |

90 | 0.05 | 0.065 | 0.007 | 0.018 | −0.209 | 0.005 | 0.017 | 0.144 | 0.015 | 0.033 | −0.075 | 0.006 | 0.016 |

0.1 | −0.144 | 0.006 | 0.020 | −0.043 | 0.009 | 0.022 | 0.273 | 0.017 | 0.039 | 0.516 | 0.010 | 0.018 | |

0.15 | 0.709 | 0.014 | 0.028 | 0.585 | 0.017 | 0.024 | 0.376 | 0.029 | 0.060 | 0.593 | 0.018 | 0.025 | |

0.2 | 0.851 | 0.028 | 0.037 | 0.644 | 0.020 | 0.032 | 0.264 | 0.062 | 0.125 | 0.691 | 0.054 | 0.033 | |

120 | 0.05 | −0.310 | 0.005 | 0.019 | −0.516 | 0.007 | 0.025 | −0.380 | 0.006 | 0.019 | −0.242 | 0.006 | 0.021 |

0.1 | 0.364 | 0.007 | 0.018 | 0.430 | 0.011 | 0.022 | 0.424 | 0.012 | 0.021 | 0.399 | 0.011 | 0.023 | |

0.15 | 0.373 | 0.018 | 0.028 | 0.342 | 0.012 | 0.027 | 0.565 | 0.021 | 0.029 | 0.429 | 0.025 | 0.037 | |

0.2 | 0.546 | 0.012 | 0.025 | 0.959 | 0.034 | 0.032 | 0.533 | 0.029 | 0.043 | 0.476 | 0.036 | 0.040 | |

150 | 0.05 | −0.256 | 0.006 | 0.020 | −0.095 | 0.009 | 0.026 | 0.103 | 0.018 | 0.053 | −0.204 | 0.005 | 0.016 |

0.1 | 0.538 | 0.008 | 0.017 | −0.272 | 0.007 | 0.023 | 0.634 | 0.011 | 0.020 | 0.477 | 0.008 | 0.017 | |

0.15 | 0.422 | 0.018 | 0.033 | 0.561 | 0.016 | 0.027 | 0.809 | 0.028 | 0.027 | 0.656 | 0.016 | 0.020 | |

0.2 | 0.594 | 0.022 | 0.030 | 0.802 | 0.037 | 0.031 | 0.564 | 0.033 | 0.033 | 0.618 | 0.049 | 0.043 |

v_{fR}[mm/s] | n [1/min] | Ssk | Vmp | Vvv | v_{fR}[mm/s] | n [1/min] | Ssk | Vmp | Vvv |
---|---|---|---|---|---|---|---|---|---|

0.007 | 31.5 | 0.264 | 0.052 | 0.121 | 0.019 | 31.5 | 0.352 | 0.053 | 0.095 |

45 | −0.078 | 0.038 | 0.118 | 45 | 0.000 | 0.040 | 0.097 | ||

63 | 0.027 | 0.050 | 0.137 | 63 | 0.438 | 0.058 | 0.113 | ||

90 | −0.101 | 0.043 | 0.110 | 90 | 0.290 | 0.066 | 0.129 | ||

0.013 | 31.5 | 0.776 | 0.058 | 0.109 | 0.030 | 31.5 | 0.521 | 0.063 | 0.122 |

45 | 0.078 | 0.058 | 0.137 | 45 | 0.023 | 0.055 | 0.120 | ||

63 | 1.832 | 0.063 | 0.108 | 63 | 0.134 | 0.051 | 0.112 | ||

90 | −0.349 | 0.056 | 0.139 | 90 | 0.322 | 0.072 | 0.134 |

**Table A3.**Standard deviations of the Vmp and Vvv values connected to negative Ssk values in hard-turned surfaces.

a_{p} [mm] | ||||
---|---|---|---|---|

0.05 | 0.1 | 0.2 | 0.3 | |

stdev_Vmp | 0.00072 | 0.0031 | 0.0014 | 0.0004 |

stdev_Vvv | 0..00094 | 0.0089 | 0.0025 | 0.0031 |

## References

- Sukaylo, V.A.; Kaldos, A.; Krukovsky, G.; Lierath, F.; Emmer, T.; Pieper, H.J.; Kundrak, J.; Bana, V. Development and verification of a computer model for thermal distortions in hard turning. J. Mater. Process. Technol.
**2004**, 155–156, 1821–1827. [Google Scholar] [CrossRef] - Zielinski, T.; Vovk, A.; Riemer, O.; Karpuschewski, B. Influence of local material loads on surface topography while machining steel 42CrMo4 and Inconel 718. Procedia CIRP
**2022**, 108, 412–417. [Google Scholar] [CrossRef] - Vrabel, M.; Eckstein, M.; Mankova, I. Analysis of the metallography parameters and residual stress induced when producing bolt holes in Inconel 718 alloy. Int. J. Adv. Manuf. Technol.
**2018**, 96, 4353–4366. [Google Scholar] [CrossRef] - Kundrak, J. Alternative machining procedures of hardened steels. Manuf. Technol.
**2011**, 11, 32–39. [Google Scholar] [CrossRef] - Mamalis, A.G.; Kundrak, J.; Horvath, M. On a novel tool life relation for precision cutting tools. J. Manuf. Sci. E–T ASME
**2005**, 127, 328–332. [Google Scholar] [CrossRef] - Martowibowo, S.Y.; Damanik, B.K. Optimization of material removal rate and surface roughness of AISI 316L under dry turning process using genetic algorithm. Manuf. Technol.
**2021**, 21, 373–380. [Google Scholar] [CrossRef] - Bilek, O.; Pata, V.; Kubisova, M.; Reznicek, M. Mathematical methods of surface roughness evaluation of areas with a distinctive inclination. Manuf. Technol.
**2018**, 18, 363–368. [Google Scholar] [CrossRef] - Sztankovics, I.; Kundrak, J. Theoretical value of total height of profile in rotational turning. Appl. Mech. Mater.
**2014**, 474, 405–410. [Google Scholar] [CrossRef] - Mathia, T.G.; Pawlus, P.; Wieczorowski, M. Recent trends in surface metrology. Wear
**2011**, 271, 494–508. [Google Scholar] [CrossRef] - Townsend, A.; Senin, N.; Blunt, L.; Leach, R.K.; Taylor, J.S. Surface texture metrology for metal additive manufacturing: A review. Precis. Eng.
**2016**, 46, 34–47. [Google Scholar] [CrossRef] - Szlachetka, O.; Witkowska-Dobrev, J.; Baryla, A.; Dohojda, M. Low-density polyethylene (LDPE) building films—Tensile properties and surface morphology. J. Build. Eng.
**2021**, 44, 103386. [Google Scholar] [CrossRef] - Flack, K.A.; Schultz, M.P.; Barros, J.M. Skin friction measurements of systematically-varied roughness: Probing the role of roughness amplitude and skewness. Flow Turbulence Combust.
**2020**, 104, 317–329. [Google Scholar] [CrossRef] - Sedlacek, M.; Gregorcic, P.; Podgornik, B. Use of the roughness parameters Ssk and Sku to control friction—A method for designing surface texturing. Tribol. Trans.
**2016**, 60, 260–266. [Google Scholar] [CrossRef] - Bingley, R.; Buttery, M.; Romera, R.F. The effect of surface production techniques on the tribological behaviour of fluid lubricants. In Proceedings of the 18 European Space Mechanisms and Tribology Symposium, Munich, Germany, 18–20 September 2019. [Google Scholar]
- Kovacs, Z.; Viharos, Z.J.; Kodacsy, J. The effects of machining strategies of magnetic assisted roller burnishing on the resulted surface structure. Mater. Sci. Eng.
**2018**, 448, 012002. [Google Scholar] [CrossRef] - Molnar, V. Tribological properties and 3d topographic parameters of hard turned and ground surfaces. Materials
**2022**, 15, 2505. [Google Scholar] [CrossRef] - Karkalos, N.E.; Karmiris-Obratanski, P.; Kurpiel, S.; Zagorski, K.; Markopoulos, A.P. Investigation on the surface quality obtained during trochoidal milling of 6082 aluminum alloy. Machines
**2021**, 9, 75. [Google Scholar] [CrossRef] - Eiselt, P.; Hirsch, S.J.; Nestler, A.; Grund, T.; Schubert, A.; Lampke, T. Influence of the kinematic roughness resulting from facing of AMC specimens on preconditioning of friction surfaces. Procedia CIRP
**2022**, 108, 1–6. [Google Scholar] [CrossRef] - Maruda, R.W.; Krolczyk, G.M.; Wojciechowski, S.; Powalka, B.; Klos, S.; Szczotkarz, N.; Matuszak, M.; Khanna, N. Evaluation of turning with different cooling-lubricating techniques in terms of surface integrity and tribologic properties. Tribol. Int.
**2020**, 148, 106334. [Google Scholar] [CrossRef] - Wdowik, R. Measurements of surface texture parameters after ultrasonic assisted and conventional grinding of carbide and ceramic samples in selected machining conditions. Procedia CIRP
**2018**, 78, 329–334. [Google Scholar] [CrossRef] - Grzesik, W.; Rech, J.; Zak, K. High-precision finishing hard steel surfaces using cutting, abrasive and burnishing operations. Procedia Manuf.
**2015**, 1, 619–627. [Google Scholar] [CrossRef] - Chen, H.; Xu, C.; Xiao, G.; Yi, M.; Chen, Z.; Zhang, J. Analysis of the relationship between roughness parameters of wear surface and tribology performance of 5CB liquid crystal. J. Mol. Liq.
**2022**, 352, 118711. [Google Scholar] [CrossRef] - Zabala, A.; Saenz de Argandona, E.; Canizares, D.; Llavori, I.; Otegi, N.; Mendiguren, J. Numerical study of advanced friction modelling for sheet metal forming: Influence of the die local roughness. Tribol. Int.
**2022**, 165, 107259. [Google Scholar] [CrossRef] - Yang, Y.; Knust, S.; Schwiderek, S.; Qin, Q.; Yun, Q.; Grundmeier, G.; Keller, A. Protein adsorption at nanorough titanium oxide surfaces: The importance of surface statistical parameters beyond surface roughness. Nanomaterials
**2021**, 11, 357. [Google Scholar] [CrossRef] [PubMed] - Zhao, Y.; Wang, G.C.; Lu, T. Characterization of Amorphous and Crystalline Rough Surface. Principles and Applications; Academic Press: San Diego, CA, USA, 2001; ISBN 9780080531380. [Google Scholar]
- Trzepiecinski, T.; Szpunar, M.; Dzierwa, A.; Zaba, K. Investigation of surface roughness in incremental sheet forming of conical drawpieces from pure titanium sheets. Materials
**2022**, 15, 4278. [Google Scholar] [CrossRef] - Orrillo, P.A.; Santalla, S.N.; Cuerno, R.; Vazquez, L.; Ribotta, S.B.; Gassa, L.M.; Mompean, F.J.; Salvarezza, R.C.; Vela, M.E. Morphological stabilization and KPZ scaling by electrochemically induced co-deposition of nanostructured NiW alloy films. Sci. Rep.
**2017**, 7, 17997. [Google Scholar] [CrossRef] - Pawlus, P.; Reizer, R.; Zelasko, W. Prediction of parameters of equivalent sum rough surfaces. Materials
**2020**, 13, 4898. [Google Scholar] [CrossRef] - Yu, N.; Polycarpou, A.A. Combining and contacting of two rough surfaces with asymmetric distribution of asperity heights. J. Tribol.
**2004**, 126, 225–232. [Google Scholar] [CrossRef] - Naylor, A.; Talwalkar, S.C.; Trail, I.A.; Joyce, T.J. Evaluating the surface topography of pyrolytic carbon finger prostheses through measurement of various roughness parameters. J. Funct. Biomater.
**2016**, 7, 9. [Google Scholar] [CrossRef] - Gadelmawla, E.S.; Koura, M.M.; Maksoud, T.M.A.; Elewa, I.M.; Soliman, H.H. Roughness parameters. J. Mater. Process. Technol.
**2002**, 123, 133–145. [Google Scholar] [CrossRef] - Sedlacek, M.; Podgornik, B.; Vizintin, J. Correlation between standard roughness parameters skewness and kurtosis and tribological behaviour of contact surfaces. Tribol. Int.
**2012**, 48, 102–112. [Google Scholar] [CrossRef] - Ba, E.C.T.; Dumont, M.R.; Martins, P.S.; Drumond, R.M.; Martins da Cruz, M.P.; Vieira, V.F. Investigation of the effects of skewness Rsk and kurtosis Rku on tribological behavior in a pin-on-disc test of surfaces machined by conventional milling and turning processes. Mater. Res.
**2021**, 24, e20200435. [Google Scholar] [CrossRef] - Dzierwa, A. Influence of surface preparation on surface topography and tribological behaviours. Arch. Civ. Mech. Eng.
**2017**, 17, 502–510. [Google Scholar] [CrossRef] - Dzierwa, A.; Pawlus, P.; Zelasko, W. The influence of disc surface topography after vapour blasting on friction and wear of sliding pairs under dry friction conditions. Coatings
**2020**, 10, 102. [Google Scholar] [CrossRef] - Liang, G.; Schmauder, S.; Lyu, M.; Schneider, Y.; Zhang, C.; Han, Y. An investigation of the influence of initial roughness on the friction and wear behavior of ground surfaces. Materials
**2018**, 11, 237. [Google Scholar] [CrossRef] - Zhua, Z.; Loub, S.; Majewski, C. Characterisation and correlation of areal surface texture with processing parameters and porosity of high speed sintered parts. Addit. Manuf.
**2020**, 36, 101402. [Google Scholar] [CrossRef] - Etsion, I. State of the art in laser surface texturing. J. Tribol.
**2005**, 127, 248–253. [Google Scholar] [CrossRef] - Jeng, Y.R.; Peng, S.R. Elastic-plastic contact behavior considering asperity interactions for surfaces with various height distributions. J. Tribol.
**2006**, 128, 245–251. [Google Scholar] [CrossRef] - Gu, H.; Jiao, L.; Yan, P.; Liang, J.; Qiu, T.; Liu, Z.; Wang, X. Effect of machined surface texture on fretting crack nucleation under radial loading in conformal contact. Tribol. Int.
**2021**, 153, 106575. [Google Scholar] [CrossRef] - Grzesik, W.; Zak, K.; Kiszka, P. Comparison of surface textures generated in hard turning and grinding operations. Procedia CIRP
**2014**, 13, 84–89. [Google Scholar] [CrossRef] - Longhai Special Steel. Available online: https://www.steelss.com/Carbon-steel/16mncr5.html (accessed on 17 March 2022).
- Pawlus, P.; Reizer, R.; Wieczorowski, M. Functional importance of surface texture parameters. Materials
**2021**, 14, 5326. [Google Scholar] [CrossRef] - Korzynski, M.; Dudek, K.; Palczak, A.; Kruczek, B.; Kocurek, P. Experimental models and correlations between surface parameters after slide diamond burnishing. Meas. Sci. Rev.
**2018**, 18, 123–129. [Google Scholar] [CrossRef] - Adamczak, S.; Zmarzly, P. Research of the influence of the 2D and 3D surface roughness parameters of bearing raceways on the vibration level. Journal of Physics: Conf. Ser.
**2019**, 1183, 012001. [Google Scholar] [CrossRef] - Das, J.; Linke, B. Evaluation and systematic selection of significant multi-scale surface roughness parameters (SRPs) as process monitoring index. J. Mater. Process. Technol.
**2017**, 244, 157–165. [Google Scholar] [CrossRef] - Liu, Y.; An, Q.; Huang, M.; Shang, D.; Bai, L. A novel modeling method of micro-topography for grinding surface based on ubiquitiform theory. Fractal Fract.
**2022**, 6, 341. [Google Scholar] [CrossRef]

**Figure 3.**Asymmetry of the surface based on the skewness parameter for (

**a**) ‘filled’ or ‘plateau-like’ and (

**b**) ‘peaky’ surfaces.

**Figure 5.**Ssk values of the hard-turned surfaces when the depth-of-cut (a

_{p}) was (

**a**) 0.05 mm and (

**b**) 0.1 mm.

**Figure 6.**Ssk values of the hard-turned surfaces when the depth-of-cut (a

_{p}) was (

**a**) 0.2 mm and (

**b**) 0.3 mm.

**Figure 8.**Comparison of surfaces with (

**a**) negative skewness (setup S25) and (

**b**) positive skewness (setup S28).

**Figure 9.**Negative skewness with low values of (

**a**) Vmp and (

**b**) Vvv (framed in red) when the surface is hard-turned at a

_{p}= 0.5 mm.

**Figure 10.**Negative skewness with low values of (

**a**) Vmp and (

**b**) Vvv (framed in red) when the surface is hard-turned at a

_{p}= 0.1 mm.

**Figure 11.**Negative skewness with low values of (

**a**) Vmp and (

**b**) Vvv (framed in red) when the surface is hard-turned at a

_{p}= 0.2 mm.

**Figure 12.**Negative skewness with low values of (

**a**) Vmp and (

**b**) Vvv (framed in red) when the surface is hard-turned at a

_{p}= 0.3 mm.

**Figure 13.**Negative skewness with low values of (

**a**) Vmp (

**b**) Vvv (framed in red) when the surface is ground.

**Table 1.**Chemical composition (DIN EN 10184:2008) and the mechanical and physical properties [42] of the machined material 16MnCr5.

Chemical Composition (%) | |||||
---|---|---|---|---|---|

C | Si | Mn | Cr | S | P |

0.14–0.19 | <0.40 | 1.00–1.30 | 0.80–1.10 | <0.035 | <0.025 |

Mechanical and physical properties | |||||

Tensile strength | Yield strength | Elongation | Thermal conductivity | Specific heat | Melting temperature |

1158 MPa | 1034 MPa | 15% | 16 W/mK | 500 J/kgK | 1370–1400 °C |

Procedure | Technological Parameter | Level | ||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | |||

Hard tuning | Depth-of-cut | a_{p} [mm] | 0.05 | 0.1 | 0.2 | 0.3 |

Cutting speed | v_{c} [m/min] | 60 | 90 | 120 | 150 | |

Feed rate | f [mm/rev] | 0.05 | 0.1 | 0.15 | 0.2 | |

Grinding | Infeed velocity | v_{fR} [mm/s] | 0.07 | 0.13 | 0.19 | 0.30 |

Revolutions per minute | n [1/min] | 31.5 | 45 | 63 | 90 |

Setup | a_{p} | v_{c} | f | Setup | a_{p} | v_{c} | f |
---|---|---|---|---|---|---|---|

S1 | 1 | 1 | 1 | S33 | 3 | 1 | 1 |

S2 | 1 | 1 | 2 | S34 | 3 | 1 | 2 |

S3 | 1 | 1 | 3 | S35 | 3 | 1 | 3 |

S4 | 1 | 1 | 4 | S36 | 3 | 1 | 4 |

S5 | 1 | 2 | 1 | S37 | 3 | 2 | 1 |

S6 | 1 | 2 | 2 | S38 | 3 | 2 | 2 |

S7 | 1 | 2 | 3 | S39 | 3 | 2 | 3 |

S8 | 1 | 2 | 4 | S40 | 3 | 2 | 4 |

S9 | 1 | 3 | 1 | S41 | 3 | 3 | 1 |

S10 | 1 | 3 | 2 | S42 | 3 | 3 | 2 |

S11 | 1 | 3 | 3 | S43 | 3 | 3 | 3 |

S12 | 1 | 3 | 4 | S44 | 3 | 3 | 4 |

S13 | 1 | 4 | 1 | S45 | 3 | 4 | 1 |

S14 | 1 | 4 | 2 | S46 | 3 | 4 | 2 |

S15 | 1 | 4 | 3 | S47 | 3 | 4 | 3 |

S16 | 1 | 4 | 4 | S48 | 3 | 4 | 4 |

S17 | 2 | 1 | 1 | S49 | 4 | 1 | 1 |

S18 | 2 | 1 | 2 | S50 | 4 | 1 | 2 |

S19 | 2 | 1 | 3 | S51 | 4 | 1 | 3 |

S20 | 2 | 1 | 4 | S52 | 4 | 1 | 4 |

S21 | 2 | 2 | 1 | S53 | 4 | 2 | 1 |

S22 | 2 | 2 | 2 | S54 | 4 | 2 | 2 |

S23 | 2 | 2 | 3 | S55 | 4 | 2 | 3 |

S24 | 2 | 2 | 4 | S56 | 4 | 2 | 4 |

S25 | 2 | 3 | 1 | S57 | 4 | 3 | 1 |

S26 | 2 | 3 | 2 | S58 | 4 | 3 | 2 |

S27 | 2 | 3 | 3 | S59 | 4 | 3 | 3 |

S28 | 2 | 3 | 4 | S60 | 4 | 3 | 4 |

S29 | 2 | 4 | 1 | S61 | 4 | 4 | 1 |

S30 | 2 | 4 | 2 | S62 | 4 | 4 | 2 |

S31 | 2 | 4 | 3 | S63 | 4 | 4 | 3 |

S32 | 2 | 4 | 4 | S64 | 4 | 4 | 4 |

Setup | S65 | S66 | S67 | S68 | S69 | S70 | S71 | S72 | S73 | S74 | S75 | S76 | S77 | S78 | S79 | S80 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

v_{fR} | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 |

n | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |

Procedure | Coefficient of Correlation ® | Quadratic Regression Function | Coefficient of Determination (R ^{2}) | |
---|---|---|---|---|

Hard turning | a_{p} = 0.05 mm | 0.62 | Vmp = 0.0228Ssk^{2} + 0.0078Ssk + 0.0063 | 0.4323 |

0.65 | Vvv = 0.0213Ssk^{2} + 0.0022Ssk + 0.0185 | 0.5334 | ||

a_{p} = 0.1 mm | 0.85 | Vmp = 0.0226Ssk^{2} + 0.0089Ssk + 0.0069 | 0.895 | |

0.66 | Vvv = 0.0068Ssk^{2} + 0.0048Ssk + 0.023 | 0.482 | ||

a_{p} = 0.2 mm | 0.41 | Vmp = − 0.0336Ssk^{2} + 0.0343Ssk + 0.0182 | 0.238 | |

0.05 | Vvv = − 0.0995Ssk^{2} + 0.0476Ssk + 0.0428 | 0.187 | ||

a_{p} = 0.3 mm | 0.62 | Vmp = 0.0716Ssk^{2} + 0.0023Ssk + 0.0042 | 0.466 | |

0.45 | Vvv = − 0.0064Ssk^{2} + 0.0158Ssk + 0.0221 | 0.20 | ||

Grinding | 0.46 | Vmp = − 0.0071Ssk^{2} + 0.0192Ssk + 0.0516 | 0.2936 | |

−0.33 | Vvv = 0.0047Ssk^{2} – 0.0161Ssk + 0.1218 | 0.1232 |

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Molnar, V. Asymmetric Height Distribution of Surfaces Machined by Hard Turning and Grinding. *Symmetry* **2022**, *14*, 1591.
https://doi.org/10.3390/sym14081591

**AMA Style**

Molnar V. Asymmetric Height Distribution of Surfaces Machined by Hard Turning and Grinding. *Symmetry*. 2022; 14(8):1591.
https://doi.org/10.3390/sym14081591

**Chicago/Turabian Style**

Molnar, Viktor. 2022. "Asymmetric Height Distribution of Surfaces Machined by Hard Turning and Grinding" *Symmetry* 14, no. 8: 1591.
https://doi.org/10.3390/sym14081591