Impact of rotational speed of composite friction pair on energy accumulation in acoustic emission signal formation

The paper considers the results of modelling acoustic emission signals that form under variations in the rotational speed of a friction pair made of a composite material. It is found that the energy accumulation in acoustic emission signals that form relative to time takes place in accordance with linear law under normal wear of a friction pair. If the rotational speed of a friction pair increases, the rates of accumulated average energy and accumulated total energy of the acoustic emission signals that form also grow. The resulting acoustic emission signals have both accumulated average energy and accumulated total energy. A comparison of these two types of energy is conducted. It is shown that the application of data averaging reduces the rate of the accumulated energy of the acoustic emission signals that form.


Introduction
Over the past few years, research of the frictional interaction between surfaces made of composite materials has been performed regularly in various countries of the world. The reason is that these materials have high tribological characteristics. This has led to wider application of composite materials in friction units in aircraft and the aerospace industry, as well as in transport, shipbuilding and other types of equipment operating under extreme conditions.
During the research of friction units made of composite materials, some traditional methods of determining the mechanical characteristics of these units are applied. Dynamic methods of researching friction units with traditional crystal structure of materials have been widely used recently. The results of research have shown that traditional methods of checking friction units are sensitive to the macro-processes in the surface layers of materials during their interaction. Thus, the information obtained according to these methods is the key factor in the development of methods of evaluating friction units, including methods of examining these units. At the same time, the availability of various types and brands of composite materials, the features of their structure, and the specifics of their destruction during friction and wear require a systematic approach to improve the reliability of inspection and examination of friction units made of composite materials. Obtaining such information is possible only when using methods that are sensitive to the micro-processes developing in the surface layers of the frictional contact of a friction unit. One method of non-destructive testing is the method of acoustic emission, which has been widely used in the technical examination of products lately. Recording acoustic emission data during frictional interaction between surface layers of materials provides an opportunity to receive a considerable amount of information about the kinetics of processes of friction and wear in progress. It should be noted that the flow and structure of acoustic emission data can change depending on variable conditions of these processes. It is necessary to add that the high sensitivity of the acoustic emission method and large volume of data recorded complicate its interpretation, so this method cannot be effectively implemented. First of all, it concerns the consequences of relationships between the parameters of processes in progress, or between parameters that characterise friction and wear processes and parameters of acoustic emission formation. As a result, some difficulties take place in the development of evaluation and diagnostic methods for friction units made of composite materials.

Research methods
Theoretical research related to the interpretation of acoustic emission data has a special meaning. This research is associated with the modelling and development of acoustic emission signals forming during friction and wear of the surface layers of composite materials. All these processes are therefore the basis for assessing the influence of various factors on acoustic emission formation, as well as for obtaining the regularities of its variable parameters that should be expected during experimental research.
Friction units of composite materials are studied in various ways and associated mainly with the selection of materials used to make interacting surfaces, selection of lubricants, optimisation of the modes of friction unit operations, and development of methods to check and evaluate friction units. Analysis of traditional mechanical characteristics (the friction moment, friction force, and friction coefficient) has shown that the use of composite materials often leads to a decrease in the friction coefficient and intensive wear of surface layers in frictional contact (Threrujirapapong et al. 2008;Terajima et al. 2009;Il-Young Kim et al. 2009;Nuruzzaman et al. 2010;Umanath et al. 2011;Bria et al. 2011). At the same time, on-going fractographic studies have revealed different mechanisms of the destruction of surface layers in frictional contact, including their fragile destruction. These types of destruction considerably decrease the tribological characteristics of friction units and indicate the initial phases of the irreversible catastrophic stage of wear. However, when using traditional methods of checking operating friction units, the observation of these stages gets complicated due to their low sensitivity and high inertness.
The acoustic emission method is used in studies of friction surfaces and wear of composite materials. The results of experimental research show that various factors can influence acoustic emissions, among them strong interaction between surfaces (pressure on a friction unit), the contact surface rate of change (rotational speed of a friction pair), lubricating layers, the geometric parameters of surface micro-elements (type and form of the roughness of surfaces in contact), the physical and mechanical properties of surface micro-elements, etc. It is necessary to emphasise the complexity of the acoustic emissions recorded during the operation of friction units made of materials with traditional structure and composite materials (Hase et al. 2009;Fan et al. 2010;Wang, Wood 2007;Polok-Rubiniec et al. 2009;Tillmann et al. 2009;Pakula 2013). Interpretation of acoustic emission formation has considerable difficulties with the further search for regularities in the variation of acoustic emission parameters, especially at the stage of normal wear. The complexity of interpreting acoustic emissions is also related to the complexity of the theoretical research of acoustic emission signals that form during friction between surfaces made of composite materials.
Some references used in this paper consider a mathematical model and modelling of resulting acoustic emission signals formed during friction between surfaces of traditional crystal structure taking into account the contact surface rate of change, influence of constant axial loading, contact surface area of interaction, size of material under plastic deformation, and predominant destruction of secondary structures of type I and II (Filonenko et al. 2008). This research allows determining the main regularities of resulting acoustic emission signal parameters when the variation of influencing factors takes place during normal wear and during the transition from normal stage of wear to irreversible catastrophic stage of wear. This suggests that the theoretical results perfectly comply with the experimental results (Filonenko et al. 2008(Filonenko et al. , 2009. The concept of FBM (fibre bundle models) can be a concept for the creation of models and research of processes of friction between surfaces made of composite materials (Shcherbakov 2002). However, most of the research this concept is used in is related to models and modelling of the destruction of elements made of composite materials under tension and shear force influence (Shcherbakov 2002;Kun et al. 2007;Raischel et al. 2005).
Research of the destruction of composite material under tension with analysis of the energy release rate of acoustic emission events has also been conducted (Shcherbakov 2002). It has been proven that when the time of the complete destruction of composite materials draws nearer, the energy release rate of acoustic emissions increases. However, at the moment of the complete destruction of a composite material, the continuality of the function can be broken, i.e. the function that describes the changes in the accumulated energy of acoustic emission events. This situation does not allow us to get an analytical expression for the model signal of acoustic emissions.
A model based on the concept of fibre bundle models and the results of the modelling of acoustic emission signals forming during the destruction of composite materials under shear load were considered (Filonenko et al. 2012). Taking into account some features of the kinetics of composite material destruction, the expression that describes this process and the expression for the acoustic emission signal that forms were obtained. It was confirmed that composite material destruction with the specified quantity of elements leads to the formation of an acoustic emission signal as a visual impulse. In this case, the basic regularities of variation in the amplitude and energy parameters of acoustic emission signals affected by various factors can be determined. These factors are the following: the rate of composite material loading, the physical and mechanical characteristics of the composite material, and the size of the elements. The expression describing an acoustic emission impulse signal forming during the period of composite material destruction under the influence of shear load is as follows: where N 0 is the initial quantity of composite material elements facing destruction; 0 υ and r are constants that depend on the physical and mechanical characteristics of the composite material; α is the rate of loading of the composite material; t is the time, t 0 is the time of the beginning of element destruction; g is the coefficient that indicates the geometrical sizes of elements; U 0 = N 0 β δ S is maximum possible displacement at the instant of the destruction of elements; β is the factor of proportionality; and δ S is a parameter having a numerical value determined by a form of a single disturbance impulse at destruction of one element and calculated as a time unit.
Expression 1, similar to the case of the destruction of secondary structures of type I and II, which is mentioned above, can be used to analyse a resulting signal forming during friction between surfaces made of composite material. In this case, it is possible to consider some small (elementary) platform S T of contact interaction in the area S overlapping the surfaces of a friction pair, within which there is a loss of a specified quantity of elements N 0 that have certain physical and mechanical characteristics and geometrical dimensions (Fig. 1). Thus, the rotational speed that provides a time-shift position of a contact interaction platform and the axial loading applied to a friction pair will determine the threshold tension at which the destruction of composite material begins. Under these conditions, it is possible to simulate the energy parameters of the resulting acoustic emission signals forming during friction between surfaces made of composite materials, taking into account the influence of various factors, one of which can be the rotational speed of the friction pair.
Given the conditions and approaches that are described above and are used to characterise the formation of an acoustic emission signal under friction and wear of frictional contact surfaces made of traditional materials, the resulting acoustic emission signal forming during friction between surfaces made of composite materials can be shown in the following form: where j is the serial number of the contact interaction area j (j = 0, 1, 2, ..., m); ( ) j j U t is the impulse acoustic emission signal forming in the contact interaction area j according to expression 1; j t is the time that j acoustic emission signal appears; and m is the number of acoustic emission impulse signals during operating time T of a friction unit. According to expression 2, the resulting acoustic emission signal is given as a sum of impulse signals forming at specified consistent time points j t during stable destruction of elementary platforms, including a specified quantity of elementary contact interactions N 0 . The change in elementary contact surfaces is determined by the rotational speed of the friction unit. The time point j t when an i acoustic emission impulse signal appears can be given as a fixed component and as a random component: where ∆t j is the time interval between the beginning of the appearance of a subsequent acoustic emission impulse signal and a preceding one, and δ is a random component of the time when each subsequent acoustic emission signal appears.
The use of the random component δ in expression 3 is caused by the dispersion that pertains to the properties of composite materials on a friction surface, as well as by the possible unstable position of platform S T of contact interaction (the platform facing destruction) in the total area S overlapping frictional contact surfaces (Fig. 1). It should be noted that the conditions described above are maintained despite the use of different patterns of contact interaction.

Results of theoretical research
Modelling the energy characteristics of the resulting acoustic emission signals can be conducted according to equation (2) using equation (3) when the rotational speed of a friction unit made of composite materials varies. All the parameters in equations (1), (2) and (3) will be given dimensionless quantities when modelling. The process of modelling will be carried out in relative units taking some certain conditions into consideration. The quantity of N 0 elements on each subsequent platform S T (Fig. 1) is a constant. It is necessary to add that these N 0 elements have an identical size. The values of parameters 0 υ  , r  and g  in expression (1) are assumed to be as follows: 0 υ  =10 6 ; r  =10 4 ; g  =0.1. The value α  is changed in the range of 200 to 600 with the step of an increment ∆α  equal to 100. The (1), this duration is determined when calculating the amplitude of a signal relative to time. Pertaining to the condition that α  = 200, the value δ  varies randomly in the range of values δ  =0…5.0×10 -7 . If the value α  increases, the duration of the acoustic emission impulse signal that forms will decrease, as proved by the results of research that was performed recently (Filonenko et al. 2012). Accordingly, the values of j t ∆  and δ  are changed proportionally to the condition that α  equals 200 for other α  values.
The modelling is carried out in several stages. The first stage includes calculations of the energy of a resulting acoustic emission signal, in particular its energy time variations, according to expression (2) and pertaining to the conditions described above. The second stage includes the calculation of the accumulated energy of acoustic emission signals and their time characteristics according to the results obtained for each accepted rotational speed of a friction unit. The third stage is to determine the influence of the rotational speed of a friction unit and the regularities of rotational speed variations on the rate of the accumulated energy of the acoustic emission signals that form.  As the analysis of the data obtained shows, the value E'  is equal to 4867.68 when α  is equal to 200. When value α  is increased 1.5 times (when α  is equal to 300),   As the analysis of the data obtained shows, if speed v is equal to 500 min -1 , the values of the rates of accumulated average energy ' E and accumulated total energy E' of acoustic emission signals that form will be taken as ' E = 2306.57 mV 2 and E' = 1.88х10 6 mV 2 . When value v is increased 1.2 times (to 600 min -1 ) the values ' E and E' increase, respectively, 1.505 and 1.498 times. This kind of increase can be observed simultaneously with the further increase in the rotational speed of a friction pair. So, if speed v is equal to 700 min -1 , the values ' E and E' will increase, respectively, 2.534 and 2.51 times. When v is increased 1.6 times (to 800 min -1 ), the values ' E and E' will increase, respectively, 3.725 and 3.71 times.
Regularities in the variations of accumulated average energy and accumulated total energy of a resulting acoustic emission signal are characterised by non-linear specific functions when the rotational speed of a friction pair made of composite materials increases.
According to the analysis of the data obtained, the coefficients of approximating expression (4) pertaining to the regularities analysed are taken as follows: a = 2.28×10 -5 , b = 2.9542 (the rate of accumulated average energy ' E of an acoustic emission signal); a = 0.01847, b = 2.9546 (the rate of accumulated total energy E' of an acoustic emission signal). The determining coefficient of the regularities received is taken as R 2 = 0.995.

Conclusions
The results of acoustic emission modelling have shown that there is a continuous linear accumulation of the energy of an acoustic emission signal resulting from friction between surfaces made of composite materials. The accumulated energy of an acoustic emission signal can be characterised by the accumulation rate.
The increase in the rate of accumulated energy of acoustic emission signals and the increase in the rotational speed of a friction pair made of composite materials have been theoretically considered and experimentally confirmed.
The statistical analysis of the data obtained and approximation of regularities in the rate variations pertaining to accumulated average energy and accumulated total energy of the resulting acoustic emission signals have been carried out. It was determined that the increase in the average energy and total energy of an acoustic emission signal can be considered identical in the investigated range of rotational speeds of a friction pair.
The results obtained during research lead us to conclude that if averaging is used, the rate of the accumulated energy of a resulting acoustic emission signal will be much less than the same rate without averaging. If one takes into consideration the inspection of friction units made of composite materials, it is clear that the accumulated average energy of acoustic emission signals ought to be used as an informative parameter of an acoustic emission signal in order to record smaller amounts of data. With this in mind, it is necessary to emphasise that the experimental results have perfectly complied with the results of theoretical research.