Neural computing for a low-frictional coatings manufacturing of aircraft engines’ piston rings

In recent years, dynamic development of small aircrafts has been observed globally. The planes are mainly intended for recreation purposes as air taxis, agricultural planes and as small cargo aircrafts. Considering the power necessary to drive the planes, piston engines are used. The costs of purchasing and using piston engines constitute another aspect that determines their use, as the costs are lower than in the case of turbine engines. The cost of fuel is the main cost component related to using combustion engines. Some tests revealed that the majority of mechanical losses in a piston engine are caused by friction in the piston–cylinder assembly, while the most of these losses result from the piston rings rubbing against the cylinder–bearing surface. It impacts the engine life and determines its service life between overhauls. Piston rings, which also remove heat from the piston to the cylinder, make the essential sealing from the point of view of friction and lubrication [1, 2].

The friction force between the surface of the piston and the cylinder–bearing surface depends on the material of the piston and bearing surface, as well as on the lubrication conditions and value of the normal force pressing the piston to the cylinder–bearing surface. The friction between the piston and the bearing surface is not a stabilized fluent friction but occurs partly under boundary conditions. The piston works with the bearing surface at an elevated temperature, which reduces oil viscosity and causes further deterioration of the friction conditions [3, 4].

Materials used for piston rings have to meet a number of requirements that tend to be contradictory. A material for piston rings should have a low coefficient of friction when sliding on the cylinder–bearing surface material, whereby the working surface of the ring should maintain high smoothness. Some additional requirements include resistance to high load within the entire range of temperatures occurring in the engine at very limited lubrication and low tendency to seizing under boundary friction conditions that may occur in the engine. A continuous surface with high smoothness should be formed on the ring surface under normal working conditions of the engine (quick wear-in). The resulting smooth surface should demonstrate high oil-wettability and should hold oil well. The material should also reveal a certain degree of self-lubrication. No large-sized particles should be separated as the material is subjected to wear. Moreover, the material should have sufficient bending and compression strength and high elasticity, with no plastic strain. Due to the presence of corrosive factors in the fuel and suctioned air, the material should reveal corrosion resistance within the entire range of the engine working temperatures [5, 6, 7, 8].

At present, there is no material that would perfectly meet all these requirements. Cast iron is the most popular material used for piston rings, as well as alloy steel is also used for making rings by cold-rolling of steel tape. In order to improve cooperation between the piston ring and the cylinder sleeve, coatings are applied. They include chromium and/or chromium–molybdenum galvanic coats as well as flame or plasma sprayed and CVD ones [9, 10, 11, 12, 13, 14]. The nitriding process is also used for surface treatment of rings made mainly of steel [15, 16, 17, 18]. Chromium-based coats are most common; however, they are also the most dangerous ones for the natural environment, as Cr⁶⁺ is used [19, 20, 21].

The alternative, innovative solution to the coatings mentioned above is low-frictional coatings on piston rings obtained in the hybrid process that combines simultaneous sintering nanoparticles MoS₂, reduced graphene oxides (rGO) with iron nitrides with the low-pressure nitriding FineLPN. Layered inclusions of nanoparticles in such coating together with the self-lubrication by hydrogen phenomenon offer the decreasing the dry friction coefficient even twice [22, 23, 24, 25]. The use of low-pressure nitriding as the dominating thermal process protects the nanoparticles against thermochemical degradations during manufacturing as well as helps to harden the top coat to the required depth and enables reaching the controlled spectrum of compressive residual stresses that is of key importance from the point of view of fatigue strength and resistance to hydrogen wear [26, 27].

FineLPN low-pressure nitriding is a nonequilibrium process, thus Fick’s diffusion law, which describes the transport of nitrogen atoms needed to create a favorable surface structure through analytical equations or numerical methods, is difficult due to the nonlinear relationship between the diffusion coefficient and the diffusion rate as well as nonsteady boundary conditions. The problem is additionally complicated by a large variety of steel and cast iron grades (different chemical alloying), which strongly influence the diffusion rate and phase transformations. The best solution in this case, as the practice and theory indicate, is a computer-aided design based on neural networks. The assumptions to the neural network model and its applications to the low-pressure nitriding of tools have been presented in several former papers [28, 29, 30, 31]. The knowledge analysis in the field shows that the use of neural networks to predict the resulting properties of the technological surface layer of steel and low-pressure-nitrided iron (LPN) for aerospace applications has not been considered so far. Despite the wide use of neural networks in the material science [32, 33], including heat treatment [34, 35, 36], in nitriding they were mainly used in gas and ion nitriding (plasma) [37, 38, 39, 40, 41]. There is no information on the models of low-pressure nitriding in the literature. The difficulty of the problem results from both the nonstationary boundary conditions (nonstationary boundary conditions also excludes the use of analytical models based on conventional mathematical equations) as well as the huge multiparametry of the phenomenon (process temperature, segmentation, segment times, numerous alloy additions, etc.). The present paper describes a neural network model and its training procedures based on data mining in the application to the monitoring and control of low-pressure nitriding process for creation of low-frictional coatings on gray irons and steels used for the piston rings manufacturing. These types of materials have so far not been the subject of optimization of the FineLPN low-pressure nitriding process. They are also not classic materials dedicated to the nitriding process, and hence the kinetics of nitrogen profile development and structural structure of these layers have not been studied yet. The aim of the work is to confirm the hypothesis that it is possible to construct an industrial application of low-pressure nitriding based on artificial neural networks and in particular to investigate the suitability of specific neural network architectures: multilayer perceptron networks (MLPs) and radial basis-based networks (RBF) for modeling of multiphase diffusion kinetics in low-pressure nitriding.

ANN are inspired from the human nervous system and are widely used toward nonlinear modeling [46, 47]. They are part of computational intelligence. The basic cell of artificial neural networks is the neuron, which refers to the structure of the living neuron. Each neuron accepts a set of numerical inputs from various sources and base on their information. Neuron stimulation is transformed by a fixed activation function (neuron transition function), and its value is the final output value (output signal) of the neuron. An artificial neural network maps even very complex functions, and its typical task is to approximate the functions of many variable functions in order to map the set of input variables to a set of output variables [48, 49]. The ways of connecting neurons between themselves and their mutual interactions resulted in creating different types of networks.

Based on research data from EN 41CrAlMo7 (1.8509), EN 42CrMo4 (1.7225), 50HS (1.5026) and PENTHOR 854 steels, the neural network calculation algorithms have been developed to predict the nitriding processes in structural steels. The training results of these networks are characterized by high training rates (training, testing and validation quality in Tables 3, 4), which gives the high probability of the nontraining outcomes to be appropriate. The validation quality of networks for constructional steels (Table 3) was lower than training and testing quality. According to the literature [60, 61, 63], it is the normal situation because during validation the networks gave answers for patterns which they never trained. Therefore, a larger validation error is not a disturbing phenomenon. This situation was not observed for networks to the cast iron nitriding predicting (Table 4). Based on data from the research on the S14, L11, XTB cast irons, the calculation algorithms based on neutron networks have been developed to predict the nitriding processes in cast iron. The training results of these networks were high. The relative errors for hardness predictions were 2% (constructional steels) and 1% (cast iron) and, respectively, 1% and 4% for predictions of effective layer thicknesses. In the case of networks with a γ′ phase thickness, the training parameters were less precise than in the case of the previous ones (15% and 40%).

Predictions obtained from the MLP artificial neural network model were subjected to a sensitivity analysis. The resolution of the control system for temperature was ± 1 °C, and the time of segment was ± 1 min. The global sensitivity analysis carried out in the Statistica [62] program showed that the most important parameters of the model are the temperature (T) and the time of the segment of endurance (segment of annealing) (D1). The effect of the altered values on the accuracy of the prediction of the hardness and the effective case depth were examined. The maximum percentage error on the validation set was found to be 7.2% and 5.5%, respectively, whereas the maximum percentage error on validation set using the actual (not altered) values was 7.3% and 5.6%. No significant variation was found.

In addition, the algorithms determining the segmentation of the nitriding process based on the surface layer guidelines have been developed parallel. The training results of these networks are clearly weaker than the networks destined for determining individual properties. The reason for this is probably insufficient network training. With the same number of patterns that were used in training of the single-output networks, three-output networks were trained here (the network generated times of three segments of the process), which probably impeded the development of the dependence between the input and output values. In the case of training sets (based on experimental data), it is possible to significantly improve the quality of their prediction by rounding the segments’ forecast periods into full hours. However, this step has not been implemented, since in the authors’ estimation this will cause a significant deterioration of the network predictions for nontraining cases. Similar results were obtained by Afzaal [64] who investigated the relationship between hardness and thickness of the nitrided layer and process parameters for gas nitriding. He suggests that the results of reverse modeling have high percentage error because the data points used for training are not unique.

In the literature, no reports were found on modeling of nitriding under reduced pressure. Genel [37] used a backpropagation (BP) algorithm to train a multilayer feed-forward, a neural network for modeling of complex linear and nonlinear relationships between ion nitrided case depth with chromium content as well as process time. Since the nature of the ion nitriding process is different from nitriding under reduced pressure, a qualitative comparison of both models is difficult. Zhecheva et al. [38] confirmed that ANN models can be created and used to correlate between processing parameters of nitriding and hardness of titanium alloys as well as it can also be used to optimize the processing parameters and alloy composition in order to achieve desired properties for various applications, but their experiments are based on gas nitriding what makes comparison impossible.

Guo et al. [65] used a BP algorithm to training model to modeling the correlation between processing parameters and properties of maraging steels. He reports a general observation that the training time increases dramatically when the number of outputs increases. This is convergent with observations taken during the creation of the above models. Therefore, setting up a series of ANN models where each model deals with only one output value significantly simplifies and speeds up the training of the ANN model.

The neural network model and its training procedures based on data mining in the application to the monitoring and control of low-pressure nitriding process for creation of low-frictional coatings on gray irons and steels used for the piston rings manufacturing were studied. On the basis of the real low-pressure nitriding processes of structural, tool and cast steels, a training base was built, and a model of the nitriding process under reduced pressure was created. The properties of nitrided layers after nitriding processes were analyzed: surface hardness, diffusion layer thickness as well as γ′ phase thickness depending on the material and chemical composition and parameters of the process: temperature and process segmentation. The hypothesis was confirmed that it is possible to construct an industrial application of low-pressure nitriding based on artificial neural networks, and in particular to investigate the suitability of specific neural network architectures: multilayer perceptron networks (MLP) and radial baseline (RBF) based networks for multiphase diffusion kinetics in low-pressure nitriding. In addition, it has been shown that constructing networks that determine single end properties of a material (constructing specialized networks) gives more accurate forecasting results than the use of general networks that simultaneously predict several material features. Additionally, it has been demonstrated that the perceptrons with nonlinear sigmoidal activation functions (MLP) map better the mathematical relationships of kinetic multiphase diffusion than radial neurons with Gaussian activation functions (RBF).