Tribo-fatigue
Tribo-Fatigue is a subdiscipline of mechanics, which studies wear-fatigue damage in and the fracture of tribo-fatigue systems. The field was founded at the junction of tribology, and mechanics of fatigue damage and fracture in materials and structural elements.
Etymology
The term Tribo-Fatigue is derived from τριβο in Greek, meaning friction, and fatigue in French and English, meaning fatigue. It was first proposed in a letter of L. А. Sosnovskiy to K.V. Frolov on September 30, 1984.. This term was first published in 1986. It is included in the Belarusian Encyclopedia and the Great Encyclopedic Dictionary.History
The sources of Tribo-Fatigue are such scientific disciplines as Friction, Tribology, Fatigue, etc.The initial stage of development ended with the holding of the first International Symposium on Tribo-Fatigue in 1993, the preparatory materials for which were published in the following references and many other works. Likewise, they are summarized in the following reference sources and many other works. Seven International Symposiums on Tribo-Fatigue were held in four countries: Belarus, Russia, China, and Ukraine. Their reports and proceedings are published in the mentioned countries. More than 2,500 scientists and experts took part in the symposiums, and 147 authors from many countries were awarded honorary diplomas "For the Contribution to Tribo-Fatigue Development." In 2010, 25 scientists and scientific coordinators from different countries were awarded with the Honorable Anniversary Sign "TRIBO-FATIGUE-25."
In 2015, a bibliographic index was published; it included 930 works on Tribo-Fatigue, including about 40 books and 12 state and interstate standards that had been developed based on the results of research in a new field. Currently, the number of works exceeds 1,100 titles.
Objects
Tribo-Fatigue studies mechanical systems where the friction process is implemented in its manifestations during rolling, sliding, slipping, impact, erosion, and the like. At the same time, friction accommodates and transfers the volume-alternating load, which is in particular cyclic. These are high-duty products. Thus, in the traditionally studied friction pair of the wheel and rail, the rail head is simultaneously subjected to alternating bending. Therefore, the performance of this system is determined by the complex wear-fatigue damage, which is the mechanical rolling fatigue. Similarly in the pair of the crankshaft and connecting rod, the shaft journal is simultaneously subjected to bending and torsion; therefore, its performance is determined by the complex WFD, which is the mechanic sliding fatigue. In a variety of shaft-and-hub joints, the shaft is additionally subjected to bending with rotation. The joints' performance is determined by the complex WFD, which is the fretting fatigue. Meanwhile, the pipe-and-fluid system, often using oil, simultaneously realizes both hydrodynamic friction and internal pressure that loads in an alternating pattern. Therefore, its performance is determined by the complex WFD, which is the mechanic corrosion fatigue, also called the corrosion-erosion fatigue.. Similarly, radiation-mechanical fatigue is characteristic of the primary circuit pipes of the nuclear power plant.A tribo-fatigue system is any friction pair where at least one of the elements is additionally and simultaneously loaded with the volume load. At least one tribo-fatigue system can be found in virtually every modern machine, such as a car; the system must be heavily loaded and largely determines the operational reliability of the product. When particular damaging phenomena such as fatigue, friction, and wear are implemented simultaneously and jointly as the complex WFD, which is studied by Tribo-Fatigue, the technical and economic significance to modern technology increases by several times. This relates to friction and wear problems, studied by tribology, and problems of fatigue damage and fracture, studied by the field concerning mechanical fatigue.
Wear-fatigue damage
Figure 2 shows the classification of the main types of wear-fatigue damage.Table 1 describes the three main classes of tribo-fatigue systems: 1) solid / solid; 2) solid / liquid; 3) solid / particles.
| Typical tribo-fatigue system | Complex damage and fracture | Definition |
| Crankpin / connecting-rod end with sliding bearing | Mechano-sliding fatigue | Wear-fatigue damage due to the effect of kinetic interaction between the phenomena of mechanical fatigue and sliding friction |
| Wheel / rail | Mechano-rolling fatigue | Wear-fatigue damage due to the effect of kinetic interaction between the phenomena of mechanical fatigue and rolling friction |
| Spline shaft / bushing | Fretting fatigue | Wear-fatigue damage due to the effect of kinetic interaction between the phenomena of mechanical fatigue and fretting |
| Propeller shaft / sea water | Mechano-corrosion fatigue | Fatigue of the material under the simultaneous effect of alternating stresses and corrosive environ¬ment |
| Turbine blades / fluid or gas flow carrying solid particles | Mechano-erosion fatigue | Wear-fatigue damage due to the effect of kinetic interaction between the phenomena of mechanical fatigue and erosion |
| Pipe / fluid flow under pressure | Corrosion-erosion fatigue | Wear-fatigue damage due to the effect of kinetic interaction between the phenomena of mechanical fatigue, corrosion and erosion |
Effects
Table 2 summarizes the subject matter of Tribo-Fatigue as compared to tribology and mechanical fatigue, the two of which are the sources of Tribo-Fatigue. There are three main effects established and studied in Tribo-Fatigue. The direct effect in Tribo-Fatigue is to study the influence of processes and conditions of friction and wear on the change in the characteristics of fatigue resistance of tribo-fatigue systems and their elements. Experiments prove that friction and wear can reduce by 3 to 7 times or more or significantly increase by 30 to 40 percent the fatigue limit σ−1 of structural elements. The back effect is the impact of alternating stresses on the change in the characteristics of friction and wear of the tribo-fatigue system and its elements. Likewise, experiments prove that cyclic stresses under the volume load excited in the contact zone can, depending on the conditions, either reduce or increase the wear resistance of a friction pair by 10 to 60 percent or more.The effect of Λ-interactions of damage is caused by normal stresses due to non-contact volume loads, which produce fatigue, and frictional stresses, which produce friction and wear. They can be illustrated by the following rule:
According to this rule, damage from contact and volume loads is non-additive: they are not summed but interact dialectically. The dialectical nature of the interaction of damage is determined by the principle of L. A. Sosnovskiy:
in which ωσ, ωτ, ωT is irreversible damage under normal, shear and thermal stresses. Λ-functions should take three classes of values to describe unity, diversity, and physical hardening-softening processes in a system. There are formulas for calculating the limiting stresses with direct and back effects, taking into account Λ-interactions of damage:
Λ-functions defined at the macro-level are similar to non-additivity parameters in q-estimation. They were used as the basis for development of the statistical theory of non-additive systems at the nano-level. They are fundamental in modern concepts of non-additive systems. The tribo-fatigue systems can be viewed as a real class of non-additive systems at the macro-level.
By taking into account the above three effects, it is possible to formulate and address the tasks of optimal management in view of economic responsibility of the WFD processes of tribo-fatigue systems as well as to calculate strength and wear resistance of high-duty mechanical systems.
Interdisciplinary results
Tribo-Fatigue has contributed to discoveries impacting other fields, including fundamental ones.- The generalized law of friction has been theoretically formulated and experimentally confirmed : in the general case, the friction force is proportional both to contact load and volume load if the latter excites cyclic stresses in the area of contact:
where p0 is the maximum value of pressure p distribution in the contact area, kσ/p is the function that depends on the correlation of stresses acting in the area of contact and caused by non-contact and contact loads, and f is the coefficient of friction according to the classic Amonton-Coulomb law. If friction is implemented in a tension zone with volume loading, fσ/p < fs, while in the compression zone, becomes fσ/p > fs. The difference between the values of fσ/p and fs reaches 10% to 50% or more, depending on the loading conditions. Practical use of the classic law for analysis of friction in tribo-fatigue systems is unjustified since it results in a significant calculation error.
- The mechanical-mathematical model of the combined stress-strain state of the tribo-fatigue system in three-dimensional setting is as such:
- Based on the statistical model of a deformable solid, a new and effective measure for the volume damage of friction pairs and tribo-fatigue systems at any stress condition has been proposed:
- The generalized energy theory of limiting states of tribo-fatigue systems can predict the occurrence of failures according to various performance criteria such as fatigue failure, unacceptable wear, and critical density of pittings. There are solutions for several particular cases. Thus the equation concerning criteria for a special case of mechanic sliding fatigue takes the following form: aσσ2+aττw2)Λσ\τ=1, where a<<1 are coefficients, which single out from the total energy, which is the energy delivered to the system. The amount of total energy is used to form the irreparable damage. Methods for calculating such coefficients have been developed. Numerous verifications of the equation showed its adequacy to experiments.
- Experimental and theoretical studies formulated nine tribo-fatigue surprises. According to a 2005 work, "the scientists could not see, understand, imagine or analytically describe" occurrences relating to "the emergence of tribo-fatigue". For example, surprise S3, a tribo-fatigue bomb, is the abnormally low resistance to fracture at fretting fatigue due to the strong interaction of a complex of weak damages. It turned out that such a surprise is found in a rotor of a unique turbine with a unit capacity of 1200 megawatts in a fusion reactor with a strong magnetic field, which was in a rocket engine with hydrogen fuel, in turn in an installation for drilling ultra-deep wells. Surprise S5, also known as the Troppy effect, is the formation of irregular residual surface undulating damage as a result of non-stationary process of elastoplastic deformation in an area of contact interaction during rolling friction. This phenomenon occurs in a wheel-and-rail system as wavy damage that occurs on the tread surface under severe operating conditions.
- Entropy in thermodynamics is a characteristic of energy dissipation. Tribo-Fatigue proposes a similar characteristic of its absorption:
System design
Principles and methods developed for the design of tribo-fatigue systems for strength, durability, reliability, and durability taking into account the risk of an operation can solve many tasks. Tribo-Fatigue moves away from the traditional design of individual parts and turns to the estimation and design of mechanical systems. With regard to the mechanic sliding fatigue of the bending shaft and sliding-surface bearing system, the following tasks can be set and practically solved:- determining the required diameter of the shaft taking into account the direct effect,
- determining the required area of contact of the system elements taking into account the back effect,
- selecting materials for both elements of the system,
- setting the requirements of the value of the friction coefficient,
- calculating the durability of the system and its elements,
- assessing the reliability of the system under given operating conditions,
- and calculating the risk factors and indicators of safe system operation.
For example, let us comment on determination of the required cross section of the shaft. Its diameter dF taken according to the known method of calculation for mechanical fatigue is assumed equal to a unity dF=1.
If the shaft is an element of the tribo-fatigue system, then the allowance for the effect of the processes of friction and wear, that are generally characterized by the relative value of friction stresses τW2/τf2, leads to the fact that in order to provide its strength reliability the value of dTF can be either significantly less or significantly more than the value of dF; it depends on the ratio between the occurring processes of hardening-softening.
The analysis of other graphs in Figure 4 leads to similar conclusions in deciding on the selection of the required area of contact, properties of a material, friction coefficient, etc.
Testing machines
A new class of testing equipment, called SI-series machines, for wear-fatigue testing of materials, models of friction pairs, and tribo-fatigue systems is based on inventions within the Tribo-Fatigue framework. The main feature of such machines is the use of standardized sizes of test objects. This ensures correct comparison of the results of tests carried out under different conditions.SI series machines are equipped with information-control system built on the basis of a personal computer. The software allows you to fully automate testing, registration of measured parameters and processing of statistical arrays of experimental data.
The SI-series machines are installed in the research laboratories of JSC "Gomselmash", JSC "Gomeltransneft Druzhba", Belarusian-Russian University in Mogilev, Belarusian State University in Minsk, and other academic institutions. Technical characteristics of the SI-series machines are regulated by the requirements of the interstate standard GOST 30755-2001 "Tribo-Fatigue. Machines for wear-fatigue tests. General technical requirements". The main test methods are standardized.
In 2018, a prototype model of a personal desktop test center on the base of the SI-series machines as a result of their miniaturization was manufactured under the government of Belarus. Such a center is planned to be used as a peripheral device for PCs in the universities. Test complexes are intended for the setting of a modern laboratory workshop for students and undergraduates as a part of the disciplines of the mechanical science, which include tribo-fatigue.
As academic discipline
Tribo-Fatigue has been introduced as a course in the curricula of several universities in Belarus since 1996 and China since 2018. Complete academic and methodological support is available. Online courses on Tribo-Fatigue are officially registered in Belarus. During the last twenty years, the course has been attended by more than 3,500 students and undergraduates, who contributed to improving the quality of training of mechanical engineers and mechanical mathematicians.Tribo-Fatigue for industry
Hi-Tech: cast knives for cutting and grinding apparatus of high-performance forage harvesters
The tribo-fatigue system “knife–clamp–bolts–base” in this apparatus works in difficult conditions: high shock-cyclic loads, contact loads and the influence of an aggressive environment. The operability of the most critical element of this system – cutting knives, in essence, largely determines the reliability and performance of combines.Figure 9 shows a drawing of knives, a diagram and a photo of their installation. The operational reliability of knives is determined by two parameters: a decrease in Δa of the width of the cutting edge and an increase in the radius of curvature r of the cutting edge. JSC "Gomselmash" and S&P Group TRIBOFATIGUE Ltd replaced steel knives with cast iron knives. The knives are made of ductile iron with spherical graphite and high fatigue resistance DITG. The results of field tests of knives are presented in Figure 10. It is seen that cast iron knives fully provide the condition for wear resistance: Δa = 17.2 mm < limΔa = 20 mm.
Figure 11 shows the results of field tests for blunting the cutting edge of a knife. Steel and cast cast iron knives were comparatively tested. It is seen that cast knives by this criterion are more efficient than steel knives: Δr = 0.19 – 0.10 = 0.09 mm, i.e. almost 2 times.
JSC "Gomselmash" and S&P Group TRIBOFATIGUE Ltd have also developed an original technique for accelerated laboratory testing of knives under conditions close to operational.
Operational reliability of the linear part of the pipeline
The pipe / fluid flow system under pressure is tribo-fatigue : the pressure during operation is repeatedly variable, and the friction of oil during movement causes corrosion-erosion wear on the inner surface of the pipe. A statistical study was conducted of changes in internal pressure in 4 sections of the “Druzhba” pipeline with a total length of 882 km. for 5 years. The sample was about 400,000 pressure values over 5 years. It was shown that the pressure swing is in the range from 0.4 to 3.7 MPa. The maximum deviation of the daily average pressure from the annual average exceeds 2 MPa, which is more than half of the largest. It turned out that the parameters of the loading process are different in different seasons of the year. Figure 12c-d shows the wall friction for a two-dimensional problem statement caused by the motion of a viscous fluid: c – distribution of the transverse component vy of the flow velocity along the pipe length ; d – tangential stresses on the pipe wall.Specialists came to the conclusion that the alternating nature of the load is the main reason for the accumulation of damage to the inner surface of the pipe. This initiates the formation of crack-like defects, the development of which during operation leads to a pipeline accident. From figure 13 it can be seen that during the period of operation before the development of the depreciation period, accidents were almost annually.
In connection with the approaching depreciation period, JSC "Gomeltransneft Druzhba" and S&P Group TRIBOFATIGUE Ltd developed a set of measures to restore the operability of such sections of the pipeline. The main ones were: stabilizing the pressure during operation and increasing the strength of the pipe material by loading with increased internal pressure. The operation of the pipeline after the depreciation period showed that there were no accidents for 12 years. The three accidents shown during this period relate to damage to the pipeline during repair and construction works. The working pressure was increased: before depreciation – 42 MPa, after depreciation – 45 MPa.
Further operation of the pipeline showed that failures of underwater sections of the pipeline may not be according to the criterion of crack resistance, but according to the criterion of wear. In this regard, an original method of wear-resistant tests of pipe steel samples in an oil medium was developed. The tests were carried out on a SI-series machine. To eliminate accidents due to wear, the underwater sections of the pipeline were reconstructed.
According to the results of the work, normative documents were developed.
Thus, the effectiveness of the “tribo-fatigue approach” to ensure the reliability of the linear sections of the “Druzhba” oil pipeline was confirmed.
Hi-Tech: cast iron rails
The wheel / rail system is tribo-fatigue: it is loaded with a spatial system of cyclic forces and simultaneously works under friction conditions . Modern production of its main element – steel rails is carried out by rolling.JSC “Gomselmash” and S&P Group TRIBOFATIGUE Ltd developed a technology for casting rails made of high-strength cast iron with spherical graphite and high fatigue resistance DITG.
On August 24, 2008 JSC “Gomselmash” and S&P Group TRIBOFATIGUE Ltd cast the first rail R65 from DITG cast iron.
By permission of the Gomel Department of the Belarusian Railway in 2012–2014 the planned operation of the experimental batch of R65 rails from the DITG was carried out on the tracks of the organized train traffic. After operational tests, the rails were dismantled for study. It was established: there was no vertical and lateral wear of the rail heads, there were no additional difficulties during operation in winter and summer, the general appearance and condition of the rails was normal, the rails can be re-stacked and operated in the existing section of the track.
According to calculations, the wear resistance of cast iron rails is approximately 1.5 times higher than steel, under the same operating conditions. This is due to the special properties of cast iron.
For accelerated laboratory tests, original physical models of the wheel / rail system were developed, which are tested on SI-series machines under conditions close to operational. For example, test specimens are cut from the rail head in such a way that they contain a surface area damaged during operation. A laboratory test procedure has been developed, during which rail corrugation is reproduced.
Thus, it is shown that cast iron rails are promising. Given the uniqueness of the railway track, experts believe that it is more rational to cast railway wheels from cast iron, especially for locomotives.
Large-sized gears
Toothed gears are a tribo-fatigue system: in the contact zone, rolling friction with slippage occurs, and in the transition zone from the tooth to the crown there is a cyclic bending. Laboratory models are shown in Figure 22. Accelerated laboratory tests of such models are carried out on SI-series machines. An example of tests is shown in Figure 23. The test method allows you to establish the conditions for the transition of failures either by the criterion of wear resistance, or by the criterion of fatigue.As a result of the studies, it was shown that steel large-sized gears of gearboxes of forage and grain harvesters manufactured by JSC “Gomselmash” can be made by casting of ductile iron with spheroidal graphite with high fatigue resistance DITG. Fifteen gearboxes were manufactured with pilot cast iron gears and serial steel gears. For each harvester, these gearboxes were installed as follows: on the one hand, a gearbox with a cast iron gears, and on the other hand, a gearbox with a steel gears. This ensured comparability of the results of field tests under the same conditions. The results of field tests are shown in Figure 24. It can be seen: the operability of cast iron large-sized gears is higher than that of steel gears.
JSC “MAZ”, OIM NASB and S&P Group TRIBOFATIGUE Ltd have also devel-oped an integrated approach to assessing the reliability of the drive axle of a MAZ-5440 truck tractor produced by the Minsk Automobile Plant.