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Article

Asymmetric Height Distribution of Surfaces Machined by Hard Turning and Grinding

Institute of Manufacturing Science, University of Miskolc, H-3515 Miskolc, Hungary
Symmetry 2022, 14(8), 1591; https://doi.org/10.3390/sym14081591
Received: 19 July 2022 / Revised: 29 July 2022 / Accepted: 31 July 2022 / Published: 2 August 2022

Abstract

:
The asymmetric height distribution of a machined surface can be useful from a tribological point of view in several cases. The purpose of this study is to analyze this asymmetry based on the 3D surface texture parameter skewness, providing technological parameter values that help in achieving favorable surfaces. A 16MnCr5 case-hardened steel (62–63 HRC) was machined by hard turning and grinding based on a comprehensive design of experiments and the topography of the surfaces was measured and analyzed. The texture parameter that informs about the height distribution of the surface points (skewness, Ssk) was compared to the volume parameters peak material volume (Vmp) and valley void volume (Vvv). The main finding is that negative Ssk values are found at low Vmp and Vvv values, which confirms the favorable tribological properties.

1. Introduction

In the automotive industry, several types of components and their surfaces have to fulfill functional requirements, e.g., load-bearing capacity or wear resistance. Surface integrity and surface quality is a widely studied area, but there are several gaps in the research to investigate and develop manufacturing technologies in the area of functional behavior of the machined parts [1]. Due to many of these functional requirements, precision-machining technologies have to be applied for machining the surfaces [2,3]. Although the number of electronic components is increasing, there is still a considerable need for conventionally machined components. Hard machining, such as grinding or hard turning, is still a developing area among the precision-manufacturing procedures. While grinding is a classic precision-machining procedure, hard turning is relatively new; concerning the achievable accuracy and surface quality, they can be considered as alternatives to each other [4]. With the appropriate selection of the cutting parameters, the specified surface quality can be achieved by not only grinding but also by hard turning [5]. As a result of grinding, the topography is random and without feed marks, but with hard turning, a relatively high material removal rate can be reached [6]. To fulfill the above-mentioned functional requirements, one of the most important areas is qualifying the surface texture. The effects of technological parameters on the surface texture have been analyzed in numerous studies, e.g., [7,8]. The present study focuses on tribology-related properties of hard-machined surfaces by using 3D surface texture parameters. The 3D characterization of surface texture is widely accepted nowadays [9] because it provides quantitative information about the topography [10].
The center point of the introduced experiment and analysis is the areal surface texture parameter, skewness (Ssk). Several research areas are connected to this texture parameter. Szlachetka et al. [11] analyzed the connections between Ssk and the physical–mechanical properties. Flack et al. [12] studied the effect of the parameter on friction and Sedlacek et al. [13] for wear mechanisms. Bingley et al. [14] obtained results in analyzing the effect of lubricants. Numerous studies have been published that identify connections between Ssk and other parameters, e.g., [15,16]. By studying 2D texture parameters for milled surfaces, Karkalos et al. found that Rsk is hardly sensitive to machining parameters [17]. Concerning the analyzed machining procedures, several experiments have been reported for turning and grinding when the functional parameter skewness is the focus of the research. For example, Eiselt et al. studied the load-bearing capacity of turned surfaces [18] and Maruda et al. evaluated turned surfaces as a result of using different lubricating solutions [19]. Wdowik analyzed the texture parameters and, within that, skewness for ultrasonic-assisted grinding [20]. Grzesik et al. compared the texture characteristics of hard-turned, ground and ball-burnished surfaces [21]. Other special areas can be found for the research of tribological properties based—among other factors—on the skewness parameter, e.g., lubrication performance [22] or metal forming [23].
The skewness parameter is the third-order standardized moment of the height distribution of the surface points [24]. It provides information about the symmetry or asymmetry of the height distribution function [25,26]. A zero-skewness surface means that the height distribution is symmetric. It was shown that the physical behavior and tribological properties of surfaces [27] and contact mechanics issues are strongly connected to higher-order moments of the height distribution; therefore, they are worth analyzing in detail [28,29]. In addition, it was found that the Ssk parameter is relatively sensitive to deep valleys or high peaks [30,31].
Sedlacek et al. [32] found that there is a high correlation between the tribological properties of contact surfaces and the Ssk parameter, so it is one that is useful in surface engineering. A negative value of the skewness implies that the surface is plateau-like. This means that the rate of the material in the peak zone is relatively high. Consequently, such a surface has a relatively high load-bearing capacity (i.e., the surface has a high bearing ratio). In addition, due to the lack of sharp peaks, the initial wear phase of the surface is short, and less debris is formed. Such a surface is more wear-resistant [13,32,33] than one with a positive or high skewness value and shows lower friction [34,35,36]. At the same time, negative skewness implies that the valleys are relatively narrow and due to the capillary effect, the surface retains lubricating material well [37,38] and the contact and lubrication conditions of the surface improve [39]. In contrary, high positive skewness leads to fretting crack nucleation [40]. Based on some studies, the lubricant distribution is better if the kurtosis (Sku) parameter of the surface is relatively high [32]; however, it was also found that from a tribological aspect, the skewness is more important than the kurtosis [33]. Based on these findings, an asymmetric, negative skewness surface is favorable from a tribological point of view [30]. In this study, the skewness parameter was compared to the peak material volume (Vmp) and valley void volume (Vvv) parameters. These provide information about the wear resistance and the fluid retention ability, respectively [41].
In this paper, the results of a comprehensive experiment and the skewness-centered analysis of the texture of the machined surfaces are introduced. Hard-turning and grinding experiments were carried out and the 3D topographies of the machined surfaces were analyzed. After the detailed description of the used material, machine tools, measurement equipment, the experimental plan and applied methods (Section 2), the results are demonstrated and discussed in Section 3. This section is organized as follows: presentation and analysis of the obtained skewness values of the machined surfaces; comparison of two surfaces with high and low skewness focusing on the volume parameters; detailed analysis of the connection between the skewness and volume parameters: calculation of coefficients of correlation and determination, and determining regression functions for the relationships. The main findings are summarized in Section 4.
The academic and industrial contributions of the findings are the following: existing research results were confirmed based on systematic experiments; the provided measurement data can be useful in further independent analyses; the paper provides experiment-based information about a material widely used in the automotive industry; and the experiments were carried out by applying machining parameters on the total ranges recommended by the tool manufacturers. The novelty of the paper is the finding that the negative skewness of the machined surfaces is connected to low (and hardly deviating) Vmp and Vvv volume parameter values.

2. Material and Methods

2.1. Material

The machined material (16MnCr5) is a case-hardened steel, applied widely in the automotive industry and suitable for precision machining. The standard chemical composition of the material and its mechanical and physical properties are summarized in Table 1. The carburizing was carried out at 900 °C for 8 h and the case hardening at 820 °C for 0.5 h. The parts were cooled in oil. After the heat treatment process, HRC values of 62–63 were obtained for the surfaces.

2.2. Machining and Experimental Plan

The experiments were carried out by hard turning and infeed grinding. For hard turning a CNC lathe, type Optiturn S600 (Optimum Hungary Ltd., Budapest, Hungary), was used, which is suitable for machining hardened surfaces. For the grinding, a universal cylindrical grinding machine type KE 250-04 was used. The type of the used turning insert was CNGA 120408TA4 and the type of the tool holder was CLNR 2525M12. For the grinding, a ceramic bound alumina wheel was used (type: KA32M5KE). Its external diameter and its width were 400 mm and 63 mm, respectively. In total, 64 external cylindrical surfaces were machined by hard turning and 16 by grinding. Four surfaces were separated on one workpiece. In Figure 1a, workpiece is shown being machined on the CNC lathe and the grinding machine.
In the hard-turning experiment, the values of three technological parameters were varied, and two parameter values in the grinding experiment. The values were chosen from the ranges recommended by the tool manufacturers. The technological parameters and their applied values are summarized in Table 2.
A full factorial experimental plan was applied, i.e., all the combinations of the parameter values were analyzed: three parameters on four levels in hard turning and two parameters on four levels in grinding. This resulted in 64 (from S1 to S64) and 16 (from S65 to S80) setups for hard turning and grinding, respectively. The design of the experiment is summarized in Table 3 and Table 4. This design approach allowed the analyzed parameter values to cover the whole recommended range.

2.3. Measurement and Texture Parameters

The textures of the surfaces were scanned and analyzed by a 3D roughness tester machine, type AltiSurf 520 (Altimet SAS, Thonon-les-Bains, France). An optical (chromatic confocal) sensor, type CL2, was used (Figure 2). The resolutions in the x- and y-directions were 2 μm and in the z-direction 0.012 μm. The measurement range in z-direction was 0–300 μm. For the evaluation of the data λc = 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.
In this study, the skewness (Ssk), the peak material volume (Vmp) and the valley void volume (Vvv) were analyzed and compared. The Ssk provides information about the degree of bias of the asperity, i.e., it indicates how asymmetric the distribution of the surface points is. The definition of this parameter is given by Equation (1). The Ssk parameter is the third-order standardized moment of the height distribution of the surface points.
S s k = 1 S q 3 1 A A Z 3 x ,   y d x d y ,
where Sq is the height parameter ‘root mean square height’ [μm]; A is the evaluated surface area [μm] and Z(x, y) is the height of one surface point [μm].
The connection between the nature of the texture and the value of Ssk is illustrated in Figure 3.
The Vmp and Vvv parameters provide information about the volume of the material and the void of the peak (upper 10%) and valley zone (lower 20%) of the surface. This is demonstrated in Figure 4.

3. Results and Discussion

The skewness parameters (Ssk) of the surfaces were analyzed as a function of the technological data. In Figure 5 and Figure 6, these values are demonstrated for hard turning for the four considered depth-of-cut (ap) 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 ap = 0.05 mm, the negative values vary between −0.31 and −0.03; for ap = 0.1 mm, between −0.52 and −0.04; for ap = 0.2 mm, between −0.38 and−0.16; and for ap = 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.
Analyzing the skewness values of the ground surfaces shows a higher level of instability in the skewness (Figure 7). Negative values were found for only three setups out of 16. These were restricted to low (0.007 or 0.013 mm/s) infeed velocities; meanwhile, the revolutions per minute of the workpiece was high (90 1/min). At the same time, both among the negative and the positive values, high deviations are observed: there are no obvious trends and outliers. The reason for this is the random nature of the ground surface. The obtained results strengthen former observations that the skewness is highly sensitive to the sporadic peaks and relatively deep, narrow valleys [28].
The other analyzed parameters, which can be calculated based on the Abbott–Firestone curve (Figure 8), are the peak material volume (Vmp) and the valley void volume (Vvv).
Vmp informs us about the wear resistance and load-bearing capacity and Vvv about the lubricant retention ability of a surface, similarly to the Ssk parameter [16]. Two surfaces (S25 and S28) were compared as an example before the detailed analysis. Both were hard-turned at ap = 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.
The numerical values of Vmp and Vvv are summarized in Table A1 and Table A2. The connections between the skewness and the volume parameters were analyzed for all of the data points of the different depth-of-cut levels, detailed in Table 5. The coefficient of correlation (r) indicates the strength of the linear connection between two variables. This value can be positive or negative. A positive value means that one variable increases with the increase in the other. A negative value means an inverse connection. The strength of the connection can be classified. For positive values, these are: 0.9 < r < 1:extremely strong; 0.7 < r < 0.9: strong; 0.4 < r < 0.7: medium; 0.2 < r < 0.4: weak; and 0 < r < 0.2: extremely weak connection. A strong connection was obtained for the Ssk-Vmp parameters of the surfaces hard-turned by a 0.1 mm depth-of-cut, while a weak connection was obtained for the Ssk-Vvv parameters of the surfaces hard-turned by a 0.2 mm depth-of-cut. A negative weak connection was obtained for the Ssk-Vvv parameters of the ground surfaces. The rest of the cases showed a positive medium connection. These results confirm that the Ssk parameter is suitable for predicting the tribological properties of contacting surfaces [44].
The quadratic regression functions of these connections were also determined. The coefficient of determination informs us about how the data points fit on the regression function and, therefore, about the quadratic strength of the connection between the two variables. It can be observed that the connection between Ssk and Vmp is extremely strong in the case of the surfaces hard-turned by a 0.1 mm depth-of-cut. The connection between Ssk and Vvv is strong in the case of the surfaces hard-turned by a 0.05 mm depth-of-cut, and between Ssk and Vvv, is weak in the case of the ground surfaces. The rest of the cases showed a medium-strength connection.
Based on these findings, it can generally be stated that the skewness (Ssk) parameter provides only guidelines for tribological properties, but due to the uncertainty of the Ssk parameter, it is not as reliable as the volume parameters describing the same properties. At the same time, a useful phenomenon can be observed in the skewness values of the hard-turned surfaces: for the surfaces with negative Ssk values, low Vmp and Vvv values were obtained. The deviation of these is relatively low (Table A3); the parameter values show no trend and, meanwhile, they are among the minimum Vmp or Vvv values. This is valid for all of the hard-turned surfaces but not for the ground ones. In Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13, this phenomenon is demonstrated, with the low Vmp and Vvv values connected to negative Ssk values framed in red.
This finding reveals that negative skewness values provide reliable information about low Vmp and Vvv values, which are favorable from a tribological point of view. At the same time, the positive Ssk values show strong uncertainty. The reason for this uncertainty is that the Ssk parameter is sensitive to the high peaks and deep valleys (third moment of the height distribution). Higher skewness values were obtained by applying higher feed rates, which leads to higher peaks of the texture. This fluctuation was confirmed by Adamczak et al., who analyzed bearing raceways and the friction properties of surfaces based on 2D and 3D roughness parameters [45]. Das et al. analyzed several parameters in parallel and found high deviations in the Ssk parameter in the case of extruded surfaces [46]. Liu et al. analyzed ground surfaces based on the Ssk parameter and also found relatively high fluctuation in the parameter value [47].

4. Conclusions

As a result of a systematic hard-machining experiment (hard turning and grinding) and 3D surface texture measurements for the material 16MnCr5, the following findings can be highlighted:
  • 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.
The study is limited to the machining of 16MnCr5; further experiments are planned for other materials. The analyzed influencing factors were the technological parameters. However, further parameters such as microhardness or residual stress are recommended to be analyzed.

Funding

This research received no external funding.

Data Availability Statement

Not applicable.

Conflicts of Interest

The author declares no conflict of interest.

Appendix A

In Table A1 and Table A2, the measured skewness and volume parameters are summarized for the hard-turned and the ground surfaces, respectively.
In Table A3, the standard deviations of the Vmp and Vvv values connected to negative Ssk values in hard-turned surfaces are collected.
Table A1. The measured Ssk [−], Vmp [ml/m2] and Vvv [ml/m2] values of the hard-turned surfaces.
Table A1. The measured Ssk [−], Vmp [ml/m2] and Vvv [ml/m2] values of the hard-turned surfaces.
vc [m/min]f [mm/rev]ap = 0.05 mmap = 0.1 mmap = 0.2 mmap = 0.3 mm
SskVmpVvvSskVmpVvvSskVmpVvvSskVmpVvv
600.05−0.0310.0070.018−0.4250.0070.0210.0430.0070.0170.0510.0090.028
0.10.4870.0090.0190.1940.0110.022−0.1580.0080.0220.3000.0100.025
0.150.6430.0170.0260.5780.0200.0300.4360.0250.0390.5230.0190.026
0.20.6520.0480.0350.5170.0200.0370.4220.0420.0470.5370.0460.035
900.050.0650.0070.018−0.2090.0050.0170.1440.0150.033−0.0750.0060.016
0.1−0.1440.0060.020−0.0430.0090.0220.2730.0170.0390.5160.0100.018
0.150.7090.0140.0280.5850.0170.0240.3760.0290.0600.5930.0180.025
0.20.8510.0280.0370.6440.0200.0320.2640.0620.1250.6910.0540.033
1200.05−0.3100.0050.019−0.5160.0070.025−0.3800.0060.019−0.2420.0060.021
0.10.3640.0070.0180.4300.0110.0220.4240.0120.0210.3990.0110.023
0.150.3730.0180.0280.3420.0120.0270.5650.0210.0290.4290.0250.037
0.20.5460.0120.0250.9590.0340.0320.5330.0290.0430.4760.0360.040
1500.05−0.2560.0060.020−0.0950.0090.0260.1030.0180.053−0.2040.0050.016
0.10.5380.0080.017−0.2720.0070.0230.6340.0110.0200.4770.0080.017
0.150.4220.0180.0330.5610.0160.0270.8090.0280.0270.6560.0160.020
0.20.5940.0220.0300.8020.0370.0310.5640.0330.0330.6180.0490.043
Table A2. The measured Ssk [−], Vmp [ml/m2] and Vvv [ml/m2] values of the ground surfaces.
Table A2. The measured Ssk [−], Vmp [ml/m2] and Vvv [ml/m2] values of the ground surfaces.
vfR
[mm/s]
n
[1/min]
SskVmpVvvvfR
[mm/s]
n
[1/min]
SskVmpVvv
0.00731.50.2640.0520.1210.01931.50.3520.0530.095
45−0.0780.0380.118450.0000.0400.097
630.0270.0500.137630.4380.0580.113
90−0.1010.0430.110900.2900.0660.129
0.01331.50.7760.0580.1090.03031.50.5210.0630.122
450.0780.0580.137450.0230.0550.120
631.8320.0630.108630.1340.0510.112
90−0.3490.0560.139900.3220.0720.134
Table A3. Standard deviations of the Vmp and Vvv values connected to negative Ssk values in hard-turned surfaces.
Table A3. Standard deviations of the Vmp and Vvv values connected to negative Ssk values in hard-turned surfaces.
ap [mm]
0.050.10.20.3
stdev_Vmp0.000720.00310.00140.0004
stdev_Vvv0..000940.00890.00250.0031

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Figure 1. Machining equipment: (a) CNC lathe, (b) grinding machine.
Figure 1. Machining equipment: (a) CNC lathe, (b) grinding machine.
Symmetry 14 01591 g001
Figure 2. The workpiece scanned by the CL2 type optical sensor.
Figure 2. The workpiece scanned by the CL2 type optical sensor.
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Figure 3. Asymmetry of the surface based on the skewness parameter for (a) ‘filled’ or ‘plateau-like’ and (b) ‘peaky’ surfaces.
Figure 3. Asymmetry of the surface based on the skewness parameter for (a) ‘filled’ or ‘plateau-like’ and (b) ‘peaky’ surfaces.
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Figure 4. Definitions of the analyzed volume parameters (Vmp and Vvv).
Figure 4. Definitions of the analyzed volume parameters (Vmp and Vvv).
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Figure 5. Ssk values of the hard-turned surfaces when the depth-of-cut (ap) was (a) 0.05 mm and (b) 0.1 mm.
Figure 5. Ssk values of the hard-turned surfaces when the depth-of-cut (ap) was (a) 0.05 mm and (b) 0.1 mm.
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Figure 6. Ssk values of the hard-turned surfaces when the depth-of-cut (ap) was (a) 0.2 mm and (b) 0.3 mm.
Figure 6. Ssk values of the hard-turned surfaces when the depth-of-cut (ap) was (a) 0.2 mm and (b) 0.3 mm.
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Figure 7. Ssk values of the ground surfaces.
Figure 7. Ssk values of the ground surfaces.
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Figure 8. Comparison of surfaces with (a) negative skewness (setup S25) and (b) positive skewness (setup S28).
Figure 8. Comparison of surfaces with (a) negative skewness (setup S25) and (b) positive skewness (setup S28).
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Figure 9. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.5 mm.
Figure 9. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.5 mm.
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Figure 10. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.1 mm.
Figure 10. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.1 mm.
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Figure 11. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.2 mm.
Figure 11. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.2 mm.
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Figure 12. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.3 mm.
Figure 12. Negative skewness with low values of (a) Vmp and (b) Vvv (framed in red) when the surface is hard-turned at ap = 0.3 mm.
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Figure 13. Negative skewness with low values of (a) Vmp (b) Vvv (framed in red) when the surface is ground.
Figure 13. Negative skewness with low values of (a) Vmp (b) Vvv (framed in red) when the surface is ground.
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Table 1. Chemical composition (DIN EN 10184:2008) and the mechanical and physical properties [42] of the machined material 16MnCr5.
Table 1. Chemical composition (DIN EN 10184:2008) and the mechanical and physical properties [42] of the machined material 16MnCr5.
Chemical Composition (%)
CSiMnCrSP
0.14–0.19<0.401.00–1.300.80–1.10<0.035<0.025
Mechanical and physical properties
Tensile strengthYield
strength
ElongationThermal
conductivity
Specific heatMelting
temperature
1158 MPa1034 MPa15%16 W/mK500 J/kgK1370–1400 °C
Table 2. Technological parameter values varied in the experiments.
Table 2. Technological parameter values varied in the experiments.
ProcedureTechnological ParameterLevel
1234
Hard tuningDepth-of-cutap [mm]0.050.10.20.3
Cutting speedvc [m/min]6090120150
Feed ratef [mm/rev]0.050.10.150.2
GrindingInfeed velocityvfR [mm/s]0.070.130.190.30
Revolutions per minuten [1/min]31.5456390
Table 3. Experimental setups based on the varied technological parameter values for hard turning.
Table 3. Experimental setups based on the varied technological parameter values for hard turning.
SetupapvcfSetupapvcf
S1111S33311
S2112S34312
S3113S35313
S4114S36314
S5121S37321
S6122S38322
S7123S39323
S8124S40324
S9131S41331
S10132S42332
S11133S43333
S12134S44334
S13141S45341
S14142S46342
S15143S47343
S16144S48344
S17211S49411
S18212S50412
S19213S51413
S20214S52414
S21221S53421
S22222S54422
S23223S55423
S24224S56424
S25231S57431
S26232S58432
S27233S59433
S28234S60434
S29241S61441
S30242S62442
S31243S63443
S32244S64444
Table 4. Experimental setups based on the varied technological parameter values for grinding.
Table 4. Experimental setups based on the varied technological parameter values for grinding.
SetupS65S66S67S68S69S70S71S72S73S74S75S76S77S78S79S80
vfR1111222233334444
n1234123412341234
Table 5. Connections between the skewness (Ssk) and the volume parameters (Vmp and Vvv).
Table 5. Connections between the skewness (Ssk) and the volume parameters (Vmp and Vvv).
ProcedureCoefficient of
Correlation ®
Quadratic Regression FunctionCoefficient of
Determination (R2)
Hard turningap = 0.05 mm0.62Vmp = 0.0228Ssk2 + 0.0078Ssk + 0.00630.4323
0.65Vvv = 0.0213Ssk2 + 0.0022Ssk + 0.01850.5334
ap = 0.1 mm0.85Vmp = 0.0226Ssk2 + 0.0089Ssk + 0.00690.895
0.66Vvv = 0.0068Ssk2 + 0.0048Ssk + 0.0230.482
ap = 0.2 mm0.41Vmp = − 0.0336Ssk2 + 0.0343Ssk + 0.01820.238
0.05Vvv = − 0.0995Ssk2 + 0.0476Ssk + 0.04280.187
ap = 0.3 mm0.62Vmp = 0.0716Ssk2 + 0.0023Ssk + 0.00420.466
0.45Vvv = − 0.0064Ssk2 + 0.0158Ssk + 0.02210.20
Grinding0.46Vmp = − 0.0071Ssk2 + 0.0192Ssk + 0.05160.2936
−0.33Vvv = 0.0047Ssk2 – 0.0161Ssk + 0.12180.1232
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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

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

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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

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