Artificial intelligence as efficient technique for ball bearing fretting wear damage prediction
Introduction
Artificial intelligence (AI) is the intelligence of machines and the branch of computer science which aims to create it. Major AI textbooks define the field as “the study and design of intelligent agents”, where an intelligent agent is a system that perceives its environment and takes actions which maximize its chances of success.
AI techniques were firstly presented in the middle 60 s. AI is not only seen in computer science and engineering [1]. It is studied and applied in various different sectors such as psychology, philosophy, neuroscience, linguistics, economics, control theory, probability, optimization and logic [2]. It can be applied to model complex relationships between inputs and outputs or to find patterns in data.
It is clear that conventional AI, which involves methods now classified as machine learning, characterized by formalism and statistical analysis was firstly used in expert systems to process large amounts of known information and to provide conclusions. Far more lately is the development of iterative techniques of learning, based on empirical data, which is the crucial part of every AI technique, is presented here and it is the main part of this paper. The subjects of computational intelligence were defined by Institute of Electrical and Electronics Engineers Computational Intelligence Society and are used here to model the behaviour of a complex and globally undefined system. Computational intelligence (CI) technique as an offshoot of AI is used to solve studied problem as it relies on heuristic algorithms and combines elements of learning, adaptation, evolution and fuzzy logic to create in some sense intelligent programs.
One of most widely used computational model is artificial neural network (ANN). Its greatest advantage depend on ability to be used as an arbitrary function approximation mechanism which ‘learns’ from observed data. However, using of ANNs is not so straightforward and relatively good understanding of the underlying theory is essential. Broad usefulness of ANN for engineering applications was presented by Bhadeshia [3]. Its successful implementation for prediction of cracking of welds, overall strength of superalloys, structural transformations in steels as well as bearing fault detection [4] and many other applications was confirmed.
ANNs, which are trainable systems mainly used for pattern recognition, are similar to the biological neural networks in the sense that the functions are performed collectively and in parallel by the units and no clear delineation of subtasks, to which various units are assigned, exists. In principal, the neural network model can be used to examine the effect of an individual input on the output parameter, especially when it is extremely difficult (or costly) to do it experimentally. Most of the publications that are using ANN to model wear deal with presenting the wear response of a tool during different machining procedures (i.e. turning, milling or boring). The influence of the machining parameters on wear of machine cutting tools (i.e. tool flank wear) under various operational conditions (cutting speed, depth of cut, etc.) was studied by means of ANN to find the balance between the wear of the tool and the efficiency of the machining procedure [5], [6], [7]. In general it was found that neural networks deduce the relationship between variables, including any interactions. In complicated cases, where a lot of variables are present, examination of the predictions reveals quantitatively and qualitatively interesting interactions.
As fretting damage recognition and quantification [8] for different, time-varying mechanical [9] and environmental loading conditions [10], is a hard problem to physically model and the correlation between the parameters and the response of the interface is non-linear so the use of artificial neural networks is justified. The first publication, which describes the usefulness of Artificial Intelligence techniques for the modelling of wear under fretting conditions was published by Velten et al. in 2001 [11] and is a direct continuation of pioneering work of Jones [12]. Short fibres reinforced polymer was examined after the contact with chromium steel ball. Randomly chosen training set and test set was used to keep the good generalization capabilities for fixed network architecture. The quality of prediction was compared with multilinear regression analysis. Recently another study on fretting at the interface for crossed-cylinder couple geometry (structural steel against bearing steel) was published by Ramesh et al. [13]. ANN was implemented by the authors to evaluate the correlation between friction and wear under various fretting conditions for different thermo-chemical and solid-lubricated coatings. To solve the problem of optimization of the network structure the rate of the error convergence was checked by changing the number of hidden layers and the learning rate.
This technique and its use for designing of different models (static and dynamic ones) is judged. In the present study the comparison between the physical models, based on regression analysis, and an empirical model, based on artificial neural network is shown. As the neural network is a regression method of which linear regression is a subset (Fig. 1) it is possible to describe the behaviour by the equation that is precise and reproducible for given set of inputs. Two ANN models are built to show the usefulness of the artificial intelligence technique for solving the static problems (backpropagation NN) and dynamic ones (recurrent NN). The problem of fretting damage in bearing-related applications is used as a case study. Bearing quality is increasingly determined by its acoustical and vibrational performance and the bearing is always in the transmission path of vibrations generated between the shaft and the bearing housing [14]. Due to small oscillatory movements the interface can get fretted and then the life of the bearing predicted by simple fatigue [15] is shortened. Both, the wear response and the coefficient of friction at the interface are modelled and the empirical models, base on the data gained from the fretting tests, are created. The static ANN model is compared with the friction dissipated energy and Archard approaches, which represent the physical description of the fretting wear behaviour, to validate the approach.
Section snippets
Experimental procedure
Tests were carried out using specific Laboratory of Tribology and Dynamics of Systems (LTDS) fretting wear apparatus (Fig. 2). An electrodynamic shaker induced the reciprocating movement with a constant frequency of 10 Hz. The upper specimen (AISI 52100—chromium steel ball) rubbed against the lower fixed flat sample (AISI 52100) to simulate ball-on-flat dry point-contact conditions [16]. The spherical samples used for the experiments had 2 different grades, which resulted in different average
Data analysis
The biggest problem for ANN is to have enough data points to learn from the examples. The purpose exists to pre-treat data to get as much knowledge as possible from meaningful data.
The second thing is that a more complicated problem must be reinforced with more examples as the complexity of the network prompts the need to build a structure with more neurons in layers. Every connection between the neurons results in new bias and weights and the minimization of the error of prediction
Physical models—regression analysis
Three wear approaches are considered in this work:
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The first one is the classically Archard's wear criterion [18] used commonly during the second half of the 20th century. The wear volume versus the product of the normal force (P) and the sliding distance (S) is introduced. Transposed to the gross slip fretting condition, the Archard's product is expressed by the following relationship:with N the number of cycles and δgi the sliding amplitude of cycle i.
The Archard's approach
Conclusions
A methodology based on artificial neural networks was applied to model the damage (wear) caused by dry fretting and to describe the dynamical frictional behaviour of the interface. Influence of various mechanical parameters on the response of the network was evaluated and is in good agreement with the physical understanding of fretting phenomenon. The superiority of Artificial Intelligence methods over classical statistical ones has been confirmed by:
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Three times lower relative mean error of the
Acknowledgements
This work was partially supported by European Committee as a part of Artificial Intelligence for Industrial Applications (AI4IA) Marie Curie FP6 Research Training Programme, Contract No. 514510. The authors would like to thank the members of the Group DFI (Durability: Fretting and Interfaces) for their technical and scientific help. The authors also would like to thank Prof. E. Ioannides (SKF Product Technical Director) for his permission to publish this article.
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