# Neuro-Fuzzy Modelling of the Metallic Surface Characterization on Linear Dry Contact between Plastic Material Reinforced with SGF and Alloyed Steel

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{2}(titanium dioxide) or graphite fibers, the technological process implies transforming the material from a solid to a plastic/liquid phase, which is achieved at temperatures above 1600 °C, with the material suffering deformation, pressing, and heating depending on the machine and the technological process.

- Nylonplast AVE Polyamide + 30% glass fibres; E
_{2A}= 40.25 MPa. - Noryl Polyamide + 20% glass fibres; E
_{2B}= 31.76 MPa. - Lexan Polycarbonate + 20% glass fibres; E
_{2C}= 42.08 MPa.

_{2}), imposing p

_{max}is provided as ${p}_{max}<0.5H$, where H is the Brinell hardness for the plastic liner, enough so that it will not be crushed. The approximate depth of the wear scar is calculated with the relation: h ≈ l

^{2}/8r

_{2}.

_{A1}= 16.3 MPa; p

_{A2}= 23.5 MPa; p

_{A3}= 28.2 MPa; p

_{A4}= 32.6 MPa; p

_{A5}= 36.4 MPa

_{B1}= 12.3 MPa; p

_{B2}= 17.4 MPa; p

_{B3}= 21.4 MPa; p

_{B4}= 24.6 MPa; p

_{B5}= 27.6 MPa

_{C1}= 16.9 MPa; p

_{C2}= 23.9 MPa: p

_{C3}= 29.3 MPa; p

_{C4}= 33.8 MPa; p

_{C5}= 37.8 MPa

_{a}), shows a strong nonlinearity due to the behavior of the elastic-plastic polymers tested. In this situation, we tried an approach to model metal surface wear through advanced data fitting algorithms, because of their ability to model very complex and strongly nonlinear phenomena. This was the qualitative–quantitative analytical approach previously achieved. The graphic processing of these results was presented in Căpitanu et al. [5].

- Mode is whether the variable is treated as a dependent or an independent variable. The contention of any modelling technique is that the dependent variables can be represented as some relation, whether explicit or implicit, of the independent variables. In the present context, the paper investigates the effect of various materials, speeds, and pressures on the depth and volume of the wear scar.
- Range shows the numerical limits of each considered variable.
- Unit displays the unit of measurement for each variable.
- Type is one of three possibilities for the nature of the variable: Numerical, categorical, or ordinal [21]. The latter is not present in the experimental dataset. Speed and pressure are obviously numerical.

_{max}, P

_{max}and Ni

_{max}—are introduced. The chosen variables have a full complement of values for each of the materials used in the experiment. The eight new variables are shown in Table 5 and Table 6.

## 3. Results

#### 3.1. Linear Regression

#### 3.2. Neural Networks

#### 3.3. Generated Fuzzy Inference System

#### 3.4. Adaptive Neuro-Fuzzy Inference Systems

#### 3.5. Model Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The functional diagram of the friction couple (

**a**) the coupling elements (

**b**) mounting the coupling to experimental equipment (

**c**) movement of the bush against the disc, where 1—cylindrical thimble; 2—steel disc sample; 3—fastening nut; 4—carrier; 5—prism to ensure parallel contact.

**Figure 9.**Fuzzy inference systems generated through (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) Fuzzy c-Means (FCM) clustering for wear depth in numerical coding.

**Figure 10.**Fuzzy inference systems generated through (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) FCM clustering for wear volume in numerical coding.

**Figure 11.**Fuzzy interference systems (FIS) fit generated through (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) FCM clustering for wear depth in binary coding.

**Figure 12.**FIS fit generated through (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) FCM clustering for wear volume in numerical coding.

**Figure 13.**Fuzzy inference systems generated through adaptive neuro-fuzzy inference systems (ANFIS) with (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) FCM clustering for wear depth in binary coding.

**Figure 14.**Fuzzy inference systems generated through ANFIS with (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) FCM clustering for wear volume in binary coding.

**Figure 15.**ANFIS fit generated through (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) FCM clustering for wear depth in binary coding.

**Figure 16.**ANFIS fit generated through (

**a**) grid partitioning; (

**b**) sub-clustering; and (

**c**) FCM clustering for wear volume in binary coding.

Variable | Mode | Type | Range | Unit |
---|---|---|---|---|

Material | Independent | Categorical | N/A | N/A |

Numerical | - | - | ||

Speed | Independent | Numerical | 18.56–153.55 | cm/s |

Pressure | Independent | Numerical | 10–50 | N |

Depth | Dependent | Numerical | 0.9–9.1 | 10^{−4} mm^{3} |

Volume | Dependent | Numerical | 0.13–3.48 | 10^{−4} mm^{3} |

Option No. | Coding | Benefits | Disadvantages |
---|---|---|---|

1 | Simple Numerical Coding | Simplest implementation | Implicitly orders labels, introducing bias. |

2 | Binary Coding | Easy to implement. Translates naturally to actual context. | Introduces multiple new variables. May cause rank deficiencies when working with matrices. |

3 | Replace with numerical | Leads to a completely numerical problem. Eliminates the issues in simple and binary coding. | Introduces many new variables. May cause dimensionality problems with small datasets. |

Material | AVE | Lexan | Noryl | C120 | Rp3 |
---|---|---|---|---|---|

AVE + 30% SGF with C120 steel | 1 | 0 | 0 | 1 | 0 |

AVE + 30% SGF with Rp3 steel | 1 | 0 | 0 | 0 | 1 |

Lexan + 20% SGF with C120 steel | 0 | 1 | 0 | 1 | 0 |

Noryl + 20% SGF with C120 steel | 0 | 0 | 1 | 1 | 0 |

Independent | Dependent | ||||||||
---|---|---|---|---|---|---|---|---|---|

Material | Speed | Pressure | A | C | R | L | N | Depth | Volume |

AVE + 30% SGF/C120 | 18.56 | 20 | 1 | 1 | 0 | 0 | 0 | 2.4798 | 0.4404 |

AVE + 30% SGF/C120 | 27.85 | 20 | 1 | 1 | 0 | 0 | 0 | 3.7076 | 0.5338 |

AVE + 30% SGF/C120 | 37.13 | 30 | 1 | 1 | 0 | 0 | 0 | 5.1336 | 0.9418 |

AVE + 30% SGF/C120 | 46.41 | 10 | 1 | 1 | 0 | 0 | 0 | 3.8871 | 0.2714 |

AVE + 30% SGF/C120 | 111.4 | 10 | 1 | 1 | 0 | 0 | 0 | 4.9482 | 0.283 |

AVE + 30% SGF/Rp3 | 18.56 | 40 | 1 | 0 | 1 | 0 | 0 | 3.9708 | 1.1247 |

AVE + 30% SGF/Rp3 | 27.85 | 20 | 1 | 0 | 1 | 0 | 0 | 3.4464 | 0.5164 |

AVE + 30% SGF/Rp3 | 37.13 | 30 | 1 | 0 | 1 | 0 | 0 | 4.2392 | 0.8627 |

AVE + 30% SGF/Rp3 | 46.41 | 20 | 1 | 0 | 1 | 0 | 0 | 4.5242 | 0.5833 |

AVE + 30% SGF/Rp3 | 46.41 | 30 | 1 | 0 | 1 | 0 | 0 | 5.0392 | 0.9377 |

Lexan + 20% SGF/C120 | 27.85 | 40 | 0 | 1 | 0 | 1 | 0 | 4.9169 | 1.1594 |

Lexan + 20% SGF/C120 | 46.41 | 10 | 0 | 1 | 0 | 1 | 0 | 4.0361 | 0.2582 |

Noryl + 20% SGF/C120 | 46.41 | 40 | 0 | 1 | 0 | 0 | 1 | 6.3271 | 2.4946 |

Noryl + 20% SGF/C120 | 55.7 | 20 | 0 | 1 | 0 | 0 | 1 | 4.3885 | 1.0289 |

Noryl + 20% SGF/C120 | 55.7 | 30 | 0 | 1 | 0 | 0 | 1 | 4.9133 | 1.6474 |

Polyamide | Weight | Absorption | Elasticity | Conductivity | Dilation |
---|---|---|---|---|---|

AVE | 1.35 | 0.8 | 80 | 0.34 | 3.3 |

Noryl | 1.27 | 0.06 | 84 | 0.196 | 2.5 |

Lexan | 1.35 | 0.16 | 86 | 0.5 | 2.68 |

Steel | S_{max} | P_{max} | Ni_{max} |
---|---|---|---|

Rp3 | 0.02 | 0.025 | 0.4 |

C120 | 0.025 | 0.03 | 0.35 |

Independent | Dependent | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Material | Sp | Pr | Wgt | Abs | Els | Cd | Dil | S | P | Ni | Dpt | Vol |

A/C120 | 18.5 | 40 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 5.48 | 1.30 |

A/C120 | 27.8 | 10 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 2.91 | 0.23 |

A/C120 | 27.8 | 40 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 6.13 | 1.37 |

A/C120 | 37.1 | 10 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 3.68 | 0.29 |

A/C120 | 46.4 | 40 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 8.54 | 1.62 |

A/C120 | 57.7 | 10 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 4.47 | 0.29 |

A/C120 | 111 | 30 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 8.00 | 1.17 |

A/C120 | 153 | 10 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.025 | 0.03 | 0.35 | 5.17 | 0.31 |

A/Rp3 | 18.5 | 40 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.02 | 0.025 | 0.4 | 3.97 | 1.12 |

A/Rp3 | 27.8 | 20 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.02 | 0.025 | 0.4 | 3.44 | 0.51 |

A/Rp3 | 37.1 | 30 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.02 | 0.025 | 0.4 | 4.23 | 0.86 |

A/Rp3 | 46.4 | 20 | 1.35 | 0.8 | 80 | 0.34 | 3.3 | 0.02 | 0.025 | 0.4 | 4.52 | 0.58 |

L/C120 | 27.8 | 40 | 1.35 | 0.16 | 86 | 0.5 | 2.6 | 0.025 | 0.03 | 0.35 | 4.91 | 1.15 |

L/C120 | 46.4 | 10 | 1.35 | 0.16 | 86 | 0.5 | 2.6 | 0.025 | 0.03 | 0.35 | 4.03 | 0.25 |

N/C120 | 46.4 | 40 | 1.27 | 0.06 | 84 | 0.19 | 2.5 | 0.025 | 0.03 | 0.35 | 6.32 | 2.49 |

N/C120 | 55.7 | 20 | 1.27 | 0.06 | 84 | 0.19 | 2.5 | 0.025 | 0.03 | 0.35 | 4.38 | 1.02 |

Binary Coding | Numerical Coding | ||||
---|---|---|---|---|---|

Features | Thetas | Features | Thetas | ||

Depth | Volume | Depth | Volume | ||

Intercept | 0.5470 | −0.1621 | Intercept | 0.1632 | 4.5657 |

Speed | 0.0339 | 0.0015 | Speed | 0.0313 | 0.0035 |

Pressure | 0.0961 | 0.0391 | Pressure | 0.1095 | 0.0450 |

AVE | 0.2615 | −0.1706 | Weight | 0.0252 | −0.1091 |

Lexan | 0.3347 | 0.1097 | Absorption | 0.0826 | −0.3794 |

Noryl | −0.3257 | −0.1250 | Elasticity | −0.0004 | −0.0373 |

C120 | 0.0184 | −0.2411 | Conductivity | 0.0394 | −0.4060 |

Rp3 | −0.2729 | 0.3989 | Dilation | 0.1059 | −0.4695 |

Smax | 0.0197 | 0.0072 | |||

Pmax | 0.0188 | 0.0062 | |||

Nimax | −0.1858 | −0.0552 |

Model | Binary Coding | Numerical Coding | ||||||
---|---|---|---|---|---|---|---|---|

Train Suite | Test Suite | Train Suite | Test Suite | |||||

MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |

Linear | 0.38528 | 0.46629 | 0.64289 | 0.54639 | 0.54483 | 0.53454 | 0.49382 | 0.50348 |

Neural | 0.07182 | 0.18512 | 0.29991 | 0.30002 | 0.52048 | 0.55583 | 0.19614 | 0.33355 |

Genfis1 | 26.306 | 4.92209 | 27.094 | 4.93573 | 29.5935 | 5.19193 | 19.64452 | 4.32411 |

Genfis2 | 0.01578 | 0.07577 | 0.19928 | 0.33022 | 0.02053 | 0.09137 | 0.27421 | 0.41283 |

Genfis3 | 0.38405 | 0.47340 | 0.56615 | 0.59409 | 0.40373 | 0.47233 | 0.51991 | 0.59842 |

ANFIS1 | 0.02162 | 0.10473 | 2.98506 | 0.78510 | ||||

ANFIS2 | 0.02265 | 0.11829 | 0.30524 | 0.43454 | 0.04433 | 0.15980 | 0.16904 | 0.35767 |

ANFIS3 | 0.19765 | 0.34180 | 0.42079 | 0.49680 | 0.11747 | 0.29467 | 0.50163 | 0.62247 |

Model | Binary Coding | Numerical Coding | ||||||
---|---|---|---|---|---|---|---|---|

Train Suite | Test Suite | Train Suite | Test Suite | |||||

MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | |

Linear | 0.06750 | 0.15916 | 0.09580 | 0.17017 | 0.11225 | 0.20713 | 0.08110 | 0.19386 |

Neural | 0.02062 | 0.10657 | 0.01620 | 0.10758 | 0.08371 | 0.17435 | 0.04756 | 0.14160 |

Genfis1 | 1.09606 | 0.86541 | 1.45574 | 0.93736 | 1.49774 | 0.98549 | 1.37690 | 0.91272 |

Genfis2 | 0.00000 | 0.00000 | 1435 | 10.48023 | 0.00965 | 0.03834 | 1.82954 | 0.56139 |

Genfis3 | 0.06648 | 0.15842 | 0.03457 | 0.11739 | 0.07857 | 0.19069 | 0.04393 | 0.16326 |

ANFIS1 | 0.00000 | 0.00017 | 1.63150 | 0.47196 | ||||

ANFIS2 | 0.00441 | 0.03373 | 0.02079 | 0.11009 | 0.00965 | 0.03821 | 0.00435 | 0.04772 |

ANFIS3 | 0.02919 | 0.11852 | 0.05496 | 0.20210 | 0.00002 | 0.00182 | 0.00043 | 0.01699 |

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**MDPI and ACS Style**

Vlădăreanu, V.; Căpitanu, L.; Vlădăreanu, L.
Neuro-Fuzzy Modelling of the Metallic Surface Characterization on Linear Dry Contact between Plastic Material Reinforced with SGF and Alloyed Steel. *Materials* **2018**, *11*, 1181.
https://doi.org/10.3390/ma11071181

**AMA Style**

Vlădăreanu V, Căpitanu L, Vlădăreanu L.
Neuro-Fuzzy Modelling of the Metallic Surface Characterization on Linear Dry Contact between Plastic Material Reinforced with SGF and Alloyed Steel. *Materials*. 2018; 11(7):1181.
https://doi.org/10.3390/ma11071181

**Chicago/Turabian Style**

Vlădăreanu, Victor, Lucian Căpitanu, and Luige Vlădăreanu.
2018. "Neuro-Fuzzy Modelling of the Metallic Surface Characterization on Linear Dry Contact between Plastic Material Reinforced with SGF and Alloyed Steel" *Materials* 11, no. 7: 1181.
https://doi.org/10.3390/ma11071181