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the Methodology of Tribo-Fatigue
Objects of studies The object of study is the first and, presumably the most essential specific attribute of a scientific discipline. It is a structural element in the mechanics of fatigue fracture. It is a friction pair in tribology. Tribo-fatigue studies active systems [3, 6]. An active system implies any mechanical system in which the process of friction is realized in its any manifestation (like in sliding, rolling, slippage, impact, etc.) and which simultaneously bears and transmits cyclic workload. Fig. 1 shows an example of two typical active systems: a wheel / rail, and a connecting rod / a crank pin. A space system of cyclic forces (stresses, deformations) appears in the zone of contact between the wheel and the rail accompanied by the process of rolling friction (including slippage). Hence, mechano-rolling fatigue should be considered as the dominating type of damage of this system in operation. A space system of cyclic stresses (deformations) may also appear in the zone of contact between the crank pin and the connecting rod due to the effect of both contact and non contact loads, but in this case in combination with the process of sliding friction. It can be termed as mechano-sliding fatigue being a dominating type of damage of this system in operation. Block shaft bearings experience pure friction, crank webs and the connecting rod experience pure fatigue. Hence, the block bearings are definitely the object of tribology (T), connecting rod or shaft webs are definitely the object of the mechanics of fatigue fracture (F), while the systems like crank-up pin / connecting rod or wheel / rails are objects of tribo-fatigue (TF). Yet, traditionally, the interests of tribology and mechanics of fatigue fracture cover also the systems of crank pins / connecting rods and wheels / rails. Later the implications will be discussed [5, 6, 9].
Figure 1 Examples of typical active systems Lets take
a look on how the serviceability of one such system is assessed in practice. Assume it is a mechanical system comprising connecting rod (with a polymeric sliding bearing) / steel crank pin. It is a common friction pair for the tribologist. Since the steel shaft does not wear in contact with a polymer, the wear resistance of the polymeric bearing is to be assessed (by calculation or experimentally). The configuration in Fig. 2 can serve for this assessment. In case p is contact pressure, then the probability of failure F(p) is determined in the general case using the criteria of wear resistance, which are usually assumed to be the wear rate I(p) and / or the durability N(p).
Figure 2 Traditional approach to the calculation of a mechanical system From the
point of view of a specialist of strength, it is the structural element or the
crank-up pin. If s
is the effective cyclic stress, then in the general case the probability of
failure F(s)
is determined (by calculation or experimentally) using the criteria of fatigue
resistance, which usually imply the fatigue limit s1
and /or fatigue life N(s). Hence, the traditional assessment of reliability of a certain mechanical system using individual criteria (either resistance to fatigue or resistance to wear) implies that the relationship between its elements (the crank-up pin « the sliding bearing) is either weak (tribology: only the friction pair is studied) or totally absent (the mechanics of fatigue strength: only an individual structural element is studied). In reality in this case a specialist in tribo-fatigue considers it as a metal-to-polymer active system, which operates in the conditions of mechano-sliding fatigue. It means that there is a force interaction between the elements of the system governed by the simultaneous and joint effect of both contact pressure p and cyclic stresses s, which are induced by non-contact loads. Then the scheme of assessment of the serviceability of the system should resemble that shown in Fig. 3.
Figure 3 To the calculation of an active system The reliability of an active system can be described with the following complex indicators: F(s, p) the probability of failure of the system determined by the probability of failure of either the shaft or the bearing, or the probability of failure of both these elements simultaneously; N(s, p) is the durability of the system determined by the durability of either the shaft or the bearing, or by the durability of these two elements simultaneously; s-1р is the fatigue limit of the shaft with the account of the effect of friction and wear processes under contact pressure p; Is(р) is the wear rate of the bearing under the effect of cyclic stresses s. The effect of friction and wear processes upon the change in characteristics of fatigue resistance of the elements of the system is termed direct effect. It is clear then that characteristic s-1р describes the direct effect quantitatively. The effect of cyclic stresses upon the characteristics of friction and wear is termed back effect. Then it is clear that the characteristic Is(р) describes the back effect quantitatively. Fig. 2 and 3 clearly show that only the active system is actually adequate to the real mechanical system to be studied, meanwhile the friction pair or the structural element are just its particular schematizations. The indicators of reliability of a studied object determined with the methods of tribo-fatigue sufficiently reflect the real conditions of its operation, meanwhile similar indicators determined with the methods of tribology or the mechanics of fatigue fracture describe the behavior of the object in idealized conditions. It also relates to such an essential characteristic as the friction coefficient. The friction
force in the active system Fs
can be considered [1, 3, 10] as a function of common friction force in sliding Fs
which appears in the circumferential direction (the object the friction
pair), and the cyclic component Fc
of the friction force which
additionally appears in the zone of contact due to the excitation of cyclic
stresses (deformations) in the axial direction (Fig. 4). Then the cyclic component of the friction coefficient is fc =
Fc / FN and the friction coefficient in the active system
where fs = Fs / FN is the usual friction coefficient in sliding.
Figure 4 Force and friction coefficient in an active system Shown above ideas are summarized in Fig. 5. On the one hand, the theories of friction, wear, lubrication were integrated into tribology (T) as an integral scientific discipline. It is natural since the friction and wear processes, including those with lubrication, really combine and interact in friction pairs. On the other hand, the mechanics of fatigue fracture (F) has emerged among general problems of dynamics, strength and stability, as a discipline of specific practical significance for modern machine building. Tribo-fatigue (TF) became essential to solve effectively complex problems of reliability (R) of the key systems of machines and equipment active systems using the most significant criteria of serviceability.
Figure 5 Tribo-fatigue as a complex scientific discipline
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