principles and methodological …...the fact that in the contact, processes of various origins...

THE ANNALS OF UNIVERSITY “DUNĂREA DE JOS“ OF GALAŢI FASCICLE VIII, 2009 (XV), ISSN 1221-4590, Issue 1

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Paper present at

International Conference on Diagnosis and Prediction in Mechanical

Engineering Systems (DIPRE’09) 22 - 23 October 2009, Galati, Romania

PRINCIPLES AND METHODOLOGICAL PECULIARITIES IN THE RESEARCH OF THE TRIBOSYSTEM WITH SLIDING ON

TRANSLATION CYCLIC MOVEMENT

Gheorghe POŞTARU1, Vasile AJDER1, Ion CRUDU2, Andrei POŞTARU1, Victor CEBAN1

1 Technical University of Moldovia, Chişinău, MOLDAVIA,

2University „Dunărea de Jos” of Galaţi, ROMANIA [email protected]

ABSTRACT The work presents methodological aspects of behavior research in the cyclical

slip tribosystems regarding the dynamics of contact processes. Taking into account the fact that in the contact, processes of various origins (mechanical, thermal, hydrodynamic, electrical, and chemical) take place and superpose, and these processes influence each other reciprocally, their dynamics may be evaluated only by using dynamic measurement systems. A non-linear mechanical oscillator with an elastic element and dissipation is used as a dynamic system. The evaluation of the tribosystem’s behaviour is made after processing and using methods of non-linear dynamics of data from time series, obtained experimentally and reduced to the coordinates of the oscillator. The suggested method allows correct evaluation and prediction of evolution of the tribosystem.

KEYWORDS: Tribosystem, tribomodel, dynamic, attractor, variety, time series,

evolution.

1. GENERAL CHARACTERISTICS OF THE TRIBOSYSTEM AND ITS

OPERATING CONDITIONS Tribosystems with sliding on translation cyclic

movement represent a wide functional and construc-tive range of the cinematic translation coupling (on of the most widely spread ones in mechanisms’ struc-ture). It immediately ensures the functionality of the couple and of the entire mechanism. This tribosystem [2, 3] as compared with other types of tribosystems has the following peculiarities determined by:

a - the cinematics of the relative motion of conjugated surfaces;

b - the construction of triboelements, the rela-tive position, shape and sizes of contact surfaces;

c - functional diversity and diversity of contact loading conditions.

The cinematic peculiarities are characterized by relative movement (fig. 1) with a variable speed V(x) of the contact on stroke L in the limits of one operation cycle. The movement of the contact on the course is accelerated on the start portions of the return zone and decelerated in the arrival zones in the same zone. The start and arrival portions are limited on x coordinates by maximum speed point Vmax.

The construction of the triboelements is determined, first of all, by the function of the tribosystem. The function and operating capacity is ensured by specific constructive peculiarities of the triboelements imposed by: the position of the contact profile generatrix on the movement direction on the course; course length L; the shape of the profile and the size of the contact in the profile. An essential constructive element is the degree of covering of the surfaces. At a low degree of covering, one of the conjugated surfaces is subjected to periodical local


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contact on the x coordinate of the course with a variable period. The duration of contact local realization is dependent on the position of point x on the course, movement direction, speed V(x) in this point and width in profile of the contact patch.

L Lin fs u p s u p

v (x )

F n

d xxF f (x ) ,

N

0

1

2

F f (x )

v (x ) ,m /s

0

0

-vm

ax+

v max

T ( x ) , °C

1 0 02 0 03 0 04 0 0

-1 0 0-2 0 0-3 0 0-4 0 0

1 ,02 ,03 ,0

-1 ,0-2 ,0-3 ,0

4 08 0

1 2 01 6 02 0 0

Fig. 1. The evolvment of the cycle of the tribosystem with cyclic translation movement of piston-cylinder

type. Among the diverse functions of the tribo-

system, some of the most relevant ones are: hermetic sealing of operation space of thermal, hydraulic and pneumatic engines cylinders and of servomecha-nisms; materials transportation; taking loads and transmitting motion in steering mechanisms. Within the tribosystem function and specific operating condi-tions, the contact is subjected to mechanical and ther-mal loads. The mode of load application, loading and movement laws in real tribosystems, which may be of the most various shapes, drastically influence their behaviour by varying the unfolding of the mechanical and thermodynamic processes, contributing to selec-tive start of other complementary contact processes of physical, chemical and structural origin [1].

The cinematic of the relative movement of contact surfaces, cycle characteristics (implicitly the repeat period and duration of local contact), loading mode, triboelements construction, shape, size and states of contact surfaces, together with characteris-tics and properties of triboelement materials in the zones of friction surface layers (from the tribological interposition of the environment) represent the determining factors of tribosystem evolution. It is under these factors that processes take place in the contact, thus evolving on diametrically opposed directions (stabilizing and destabilizing). This aspect points out the ambiguous character of the evolution that imposes special requirements on the stability of

tribological properties of the materials, on contact processes dynamics and mechanical system dynamics in general. It is namely the friction forces that represent the main source of perturbations on mechanisms’ elements. In case of rising loads, the perturbations move to a nonlinear domain where conditions for a non-controllable chaotic dynamic behaviour mode may be created, that may have unpredictable consequences for the mechanical system, as well as for the tribosystem [4]. This is the reason why the funda-mental equation system in dynamics has expanded into including non-linear components of the vector function of the tribologic link force system [5, 7]. The reduced dynamic model reduced to the mobile triboelement has the following form:

2

2 ( , , , )d X dX dXm h c X F X V p Udt dtdt

+ + ⋅ = + (1)

Where: T1 2X { X ,X }= is the vector of current

coordinates of the mobile triboelement in the zone of interposition environment (layer);

1 2( , , , ) { ( , , , ), ( , , , )}TdX dX dXF X V p F X V p F X V pdt dt dt

=

the vector of interaction functions in the tribo-logical link on directions normal X1 and tangential X2;

1 2{ , , }kp p p p= ⋅⋅⋅ - nonlinear components of the parameters of the interaction function vector;

m , h ,c - matrix of the masses, of dissipation factors and of system elements rigidity;

U – vector of contact external loads and of external parameters;

V=V(x) – sliding speed of the contact. In [5] solutions for a constant sliding speed and

constant load are suggested. The situations become more complicated in the

case of sliding with a cyclic and variable relative speed of the contact.

The issues of searching and predicting condi-tions for ensuring stability in the operation of this type of tribosystems were underlined and stressed in connection with the huge flux of new materials being elaborated, that have presumably advanced tribologi-cal properties, as new technologies are used, inclu-ding nanotechnology. There are such materials on the market, but for the moment there are no argumenta-tions for their properties by means of fundamental research, either theoretical or experimental. Solving these problems imposes non-traditional approaches concerning research methods.

2. PRINCIPLES OF MODELLING AND

METHODOLOGICAL PECULIARITIES OF RESEARCH The experimental data previously obtained from

testing on tribomodels outline the existence (in the limits of the cycle) of different regimes of friction-


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lubrication. These modes and complementary contact processes directly influence the structural evolution of interposition layer 3 between con-tact surfaces of triboelements 1 and 2 (fig. 2). It is the structure and state of the interposition layer (tribolayer) that determine the rigidity of the contact (components c22 reduced to triboelement 1) and processes of dissipating (h22 factors) mechanical energy, attributing them the main role in the dynamic behaviour of the entire system. The structural changes in the tribolayer and their limits permanently influence the friction-lubrication modes. On one hand, the limit of interposition layer 3 is established by the fluid mode of friction-lubrication and takes the form of lubricant film in the contact (of hydrostatic or hydrodynamic origin), and on the other hand, it depends on the dry friction mode that repre-sents a complex structure limited by the deformation zones of the contact surface layers of the triboele-ments. The dynamic model for these two limits has been successfully determined as systems of different-tial or algebraic equations that offer determinist solutions to states that the tribosystem goes through in the process of evolution.

h22

U1

U2

c11

h11X1

X2

c22

Sup. F1F2

X V(X)

3 21

Fig. 2. Model of a tribosystem with

cyclic contact slide

Still, a number of problems is imposed by the middle range between limits (dominated by the mixed mode and friction limit), where the structure of the interposition layer may be especially complex depen-ding on: structure, chemical composition and material properties of body surfaces 1 and 2, of the lubricant and of work environment. For certain values of varia-bles and system parameters, the balance between structural generation and degradation processes of the interposition layer may become very small, degenera-ting into instabilities with aperiodical and random fluctuations. In these cases, elaborating a dynamic evolution model that would be able to reflect the whole complex of processes and their unfolding in the contact zone, encounters certain theoretical diffi-culties. They consist in determining the origins of the contact processes on the evolution axis, of the number of differential equations (number of variables), initial conditions of system sensitivity to these conditions.

This is the reason why the dynamic model may be only reconstructed on the basis of experimental data obtained while researching on real tribosystems or on models.

In actual tribosystems of mechanisms, due to the constructive inconvenience and to the reduced accessi-bility, as a rule, only a limited number of variables may be observed, considerably diminishing the truthfulness of evaluating states that the contact goes through. And in some constructions, the access to observation is impossible. The issue of accessibility is solved by a physical model of the tribosystem.

Analysing the results, the following conditions could be given:

- abiding to the cinematic of contact movement on the stroke;

- abiding to specific constructive peculiarities of triboelements;

- abiding to contact load conditions (parameters U1 and U2);

- similarity of contact processes (as results of interactions F1 and F2);

- establishing the variables and parameters of the system for real time observation;

- correct choice of friction force measurement (elements of matrixes c11 and h11) and determining the dynamic behaviour in different excitation conditions;

- choosing or elaborating an adequate method for processing, analysis, presentation and interpreta-tion of experimental data.

A truthful picture of contact evolution from the physical point of view may be determined only by means of a “dynamic device” for measurement, able to instantly perceive the state of the contact. In the process of modeling, this dynamic device may be the mechanical oscillator with an elastic element with dissipation and supplementary nonlinear connection with the tribosystem by means of the contact. Being excited by the tribosystem, the oscillator will reflect the stat of the contact in its movement trajectory.

In a tribosystem model, the oscillator having a generalized mass m consists of triboelement 1 and elastic measurer of friction force (fig. 2) having rigidity c11 and dissipation factor h11. By means of tribolayer 3 having contact rigidity c22 and dissipation factor in contact h22 a mobile connection with triboelement 2 is formed. Rigidity and dissipation factors of the oscillator influence reciprocally the factors of the interposition tribolayer creating elements of matrixes c12, c21 and h12, h21. Under the influence of loads U, the oscillator forcefully moves on direction x in the limits of the strokes L of the cycle with variable speed V(x) and executes local relative oscillations with small amplitude on directions x1 and x2 excited by interposition forces of interaction F in the contact.

The dynamics of the oscillator may truthfully reflect the state and behaviour of the tribosystem or may distort it depending on the ration between mass m and components of matrixes cij and hij, as well as on operating conditions. This imposes a careful


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choice of the construction and constructive para-meters of the elastic element.

In general, the oscillator dynamics may be des-cribed with equation system (1). In actual conditions the system may have two modes of movement: slow and fast.

For slow “quasi-static” movement, the system (1) is simplified becoming

dXcX F( X , ,V , p ) Udt

= + (2)

From this, a conclusion may be drawn that in “quasi-static” operating conditions of tribosystems the local friction force may be considered directly proportional to the elongation of the oscillator and be measured without essential distortions.

Another issue of modeling refers to the determination of variables and parameters of the system. This problem finds its answer in the analysis of tribosystem interactions.

Fig. 3. Cycle of the time series (1- friction force; 2-lubricant layer thickness) for different values of the

command (3-6).

Taking into account the cinematic aspect (fig. 1), the state of the tribosystem is evaluated together with two groups of variables, local and global [3]. Locally, within the cycle, the state of the system is determined by the immediate values of the variables vector in the zone of point x of stroke L. The following variables are important for the system: x - contact movement on the stroke; x1, x2- local relative elongations in point x of the oscillator centre of masses, correspond-ding on the normal movement and tangential to it; V(x)- local speed of sliding on the stroke; v(x1), v(x2)- local relative speeds in point x of the oscillator centre of masses, corresponding on the normal movement and tangential to it; Ff(x)- local friction force; thickness h(x) of lubricant layer (in case

of fluid mode of lubrication); local temperature in contact zone.

The state of the system is influenced by a series of external parameters (command) U and internal p (intrinsic parameters of tribological connections). The law and degree of contact load is determined with the help of command external parameters. The most important command parameters of the given tribosystem are: external force (Fn) on the normal direction of the contact surface and sliding cyclic frequency of the contact (nc). The internal parameters at the local level are determined by the macro and micro geometry of the contact surfaces, the structure, chemical composition and physical and mechanical characteristics of triboelement materials.

The components of internal parameters are influenced by both external ones and by the state of interactions F1, F2 and first of all by the energy state.

The experimental data obtained on the model are arranged as time series of dynamic variables for different values and variation laws of command parameters. As items of series, the following is accepted – the variation cycle of variables on stroke because the cycle represents a basic global informative unit of contact state (fig. 3).

In order to process and analyze time series, the trajectories of dynamic variables in the limits of the cycle are reconstructed in the spaces of the states.

In a quasi-static operating mode, the following are used as coordinates of state spaces: friction force Ff(x); contact movement x on stroke; contact sliding speed on stroke V(x) (fig. 4, 5).

Fig. 4. Cycle trajectory reconstructed in the space of coordinate states: friction force – contact

movement on stroke.

-vm ax + vm ax

0 v (x), m /s1.0 2.0 3.0-1 .0-2 .0-3 .0

F f (x),N

100

200

300

-100

-200

-300

Fig. 5. Cycle trajectory reconstructed in the states space in coordinates: friction force – sliding speed.


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The local energetic state defined by elementary work ∆ Af(x) and power P(x) dissipated on friction forces at the movement of the contact in the zone of coordinate point x is determined as a result of pro-cessing variables’ data from the space of states accor-ding to relations 3 and 4.

x b/ 2

f ( x ) fx b / 2

A F ( x )dx∆+

−

= ∫ (3)

fP( x ) F ( x ) V( x )= × (4) where: b is the contact width.

The topology of friction forces trajectories in the states space together with energetic parameters of dissipation represent the primary information source of system behavior in the limits of the cycle.

As a result of dissipation process, in the course of long periods of time there appear internal accumulations of energy in the elements of the system, which are distributed by diffusion and transfer from local spaces into the global space.

Destabilizations occur of both local (of high and medium frequency) and global (of low frequency) nature when reaching critical values like energetical threshold of the materials.

More specifically, the global energetic state deter-mines the direction of evolution of the interposition layer by means of which the tribologic connection between elements is achieved. The stability and balance of contact processes depend on the state and properties of the tribologic connection. This is the reason why the issue of studying the dynamics of interposition layer and of the tribologic connection in the whole of contact processes under the influence of system parameters becomes highly important.

This problem imposes system formalization in the vector of dynamic variables and of parameters characteristic to the global level. In cyclic movement tribosystems the global state is generalized at the level of the work cycle which includes the entire range of contact states. The vector of global dynamic variables fully determines the direction of the evolution of the tribosystem.

In order to evaluate the energetic state as a global dynamic variable the “dissipated mechanical energy” Afc is accepted, which is equivalent to the work formed at the overcoming of friction forces in the limits of a cycle, that is determined by integrating local friction forces Ff(x) at contact movement on strokes according to relation (5).

2L

f ( c ) f0

A F ( x ) dx= ∫ (5)

2L

0

1T T( x )dx2L

= ∫ (6)

The dissipated energy contributes to: modification of the thermodynamic state of the contact; structural modifications of the interposition state; wear of contact surfaces of the triboelements.

An important role in contact processes is played by the temperature. The average temperature value T in the contact zone is determined by integrating it within the limits of the cycle according to relation 6.

The dissipated energy Afc and cycle average temperature T are used as items of time series of the evolution of interposition layer (fig. 6). A fc, J

0

10

20

30

40

50

0

40

80

120

160

200

10 20 30

T , °C

2

1

t, m in Fig. 6. Time series and their corellation in time: 1-of

friction forces work Afc; 2-of temperature T in contact zone.

Energy fluctuations on certain segments of the

evolution trajectory lead to correlative essential fluctuations of the temperature. Due to this correlation, the temperature series may be successfully used as a complementary factor for evaluating contact evolution in conditions of loss of dynamic stability (fig. 7).

At fast movements, instable evolutions and dynamic behaviour the reciprocal influence between the tribosystem and the oscillator are intensified. The state of the tribosystem in these situations (described by dynamic system – (1)) may be experimentally evaluated only at a qualitative level by means of studying the dynamic behaviour of the oscillator on motion directions x1 and x2. (fig. 2).

Additional information may be obtained after an analysis of the thermodynamic state of the contact or from signals of acoustic and exo-electronic emissions, in case they are registered.

Due to technical reasons, in certain cases measurements of oscillations on normal direction x1 of the contact surface is difficult to perform. That is why in these cases it is recommended to build time series using only the oscillation cycle on tangential direction x2 as n “item”. Each oscillation cycle bears complete information about interactions and contact state in the course of performance.

Fig. 7. Temperature variation series in contact zone at

system destabilization.


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Cycle analysis and information extraction may be achieved in various aspects (energetic, spectral; oscillation form and amplitude; local jumps). A typical oscillogram of the cycle on x2 coordinate and is shown in figure 8. On its basis it can be deduced a complex and non-stationary trajectory of variable x2(x) at movement on course L.

Fig. 8. Typical oscillogram of the cycle on x2

coordinate and characteristics points a2.

The issue of correct choice of dynamic variables is important for evaluating the dynamic evolution of the contact and of interposition layer state. Within the cycle it is the ranges of elongations of characteristic points ‹a2›, a2(max) and a2(min) that are significant. The integrated average range ‹a2› determined from relation (7) is implicitly the energetic state of the contact , the form and spectrum of cycle oscillations frequency.

( )2L

2 20

1a x x dxL

⟨ ⟩ = ∫ (7)

The elongation range of maximum jumps a2(max) and of points of minimum proximity a2(min) within the cycle limits are predicting “markers” of evolution direction. Using these factors, it is possible to determine moments imminent to dynamic destabilization and of possible critical situations of contact surface gripping. Such an approach to dynamic variable choice is justified by reflecting various situations within the contact and simplifying processing methods of time series, as well as by excluding the influence of systematic errors on the measurement results of experimental data.

The characteristic points of cycle ‹a2›, a2(max) and a2(min) are used as items in order to reconstruct the time series of cycle trajectories in discrete time series (fig. 9). The new series that are obtained are significantly simplified preserving the properties of the basic series.

The issues of evaluating and predicting states and behaviour of the tribosystem in the process of evolution, as well of reconstructing the dynamic model are solved by establishing an appropriate method of processing time series of dynamic variables. Nowadays the methodology of processing

and analysis of time series has achieved a great development both at the fundamental level and on the applied one. The latter is successfully used in solving problems of non-linear dynamics [4, 5, 7]. These methods create a new methodological base for studying the behaviour of tribosystems from the dynamic aspect. This methodology helps finding points and conditions of „balance and stability” for the system. The properties of tribologic connections influenced by nonlinear contact processes are reflected in system behaviour (stable or unstable) in the proximity of these points. When achieving an asymptotic stability on relatively long periods of time, the set of states in the variable space of the tribosystem converges towards a limit variety called attractor. The attractors may be of different types: stable focus point, limit cycle-line, more complicated varieties and sets that have a fractal structure – chaotic attractor.

Fig. 9. Time series sequence reconstructed for items:

1-‹a2›; 2- a2(max); 3- a2(min).

A dynamic system may have a lot of attractors. Leaving the current attractor pool is performed by means of bifurcation points. In these points, the tribosystem qualitatively changes its internal structure. Further evolution towards stability will be done towards another attractor with a different attractor pool, different from the previous one.

Researching attractors allows for evaluating the behaviour, complexity and structure of the system on evolution trajectory. Here appears the problem of choosing variables’ space which contains the set of states that the system goes through in the process of evolution. As variables, coordinates may become values by which the process and their derivatives are appreciated. The space obtained is called state space or phase space.

The method suggested for the system under investigation makes use of time series values as variables. Judging on the fact that the series repre-sents the variation in time of just one value, and the real system, as a rule, is included in a multidimensi-

a2(max) a 2(min)

x2(x)

x 2

PMS PMS PMI

dx x

L L

‹a2›


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onal space, the phase space, according to Tackens theorem, is obtained being used as additional coordi-nates. The coordinate of the series value is given by phase translation with a discrete period of time nτ as referred to reference point t, where n-is an integer number. The obtained space will have dimension n+1. A discrete variety of Poincaré type, of variable series a2 in a plane of this space is shown in figure 10.

Fig. 10. Discreet varieties built in phase plane

obtained by phase movement τ of series trajectories: 1-‹a2›; 2- a2(max); 3- a2(min).; 4-attraction pool.

The structure of the dynamic system and the

fractal dimension of the attractor is determined by extending the dimension of phase space. The attractor located in this space is also called “quasi-attractor”. The quasi-attractor preserves the fractal dimension and the spectrum of superior Liapunov indices of the original attractor.

If the dynamic stability is lost, the evolution trajectory leaves the current attraction pool and heads towards a domain with unpredictable direction, dominated my chaotic movement [4]. The new direction will be established depending on the relation between the partial or full realizations of external and internal factors that will transit the tribosystem into qualitatively new structures (possibly self-organised ones). The study of dynamic behaviour becomes more complicated and requires other methods and analysis instruments of time series, by means of which it is possible to predict further direction of evolution and preventing critical (gripping) states in the operation of tribosystems. These issues are especially complicated and there are not established general methods of solving them. In this respect the method elaborated in [6] named by authors Flicker-Noise Spectroscopy – FNS is promising. This method has at the basis the problem of determining the informative level in the signals of time series. But even here there is a necessity of new studies in the sphere of signal processing and information techno-logies, especially those particularly connected to dynamic behaviour in the evolution of tribosystems.

In order to perform those studies, it is necessary to achieve the following objectives:

- elaborating a computer system for measure-ment, command and control of variables and tribosys-tem parameters;

- creating a database for gathering and storing of experimental data;

- elaborating methods of processing time series and varieties of states in the phase space of these series;

- elaborating and intelligent system which, by means of learning, will be able to recognize and take decisions upon structure, behaviour and evolution direction of the tribosystem.

At present, in this area research has been commenced concerning endowing the method with a computer system for experiment support.

3. CONCLUSIONS

The dynamic character of contact processes in

tribosystems with sliding on translation cyclic movement imposes new approaches in the process of elaborating research methods. Obtaining an adequate picture of contact state and of evolution direction can be achieved only with a dynamic measurement system. In the process of modeling, a nonlinear mechanical oscillator with an elastic element and dissipation is employed. The dynamic behaviour and the evolution direction of the tribosystem are evaluated after processing time series of experimental data gathered in tribomodel trials. In dynamic stability operating mode, the state and evolution of the system are evaluated by analysing of state attractors in phase space. The evaluation in non-stationary and transition modes requires additional particular research in the sphere of signal processing and informational technologies.

REFERENCES

1. Ajder V, Crudu I, Poştaru Gh.. Tomescu L. 1994, Tribo-modelling the contact between piston-ring and cilinder in internal combustion engines, Acta Tribologica, vol. 2, no. 1/1994, Univer-sity of Suceava, Romania, pp. 73-77. 2. Crudu I. On the Concept of Tribo-System and a Tribomodelling Criterion, Proc. of 4th European Tribology Congress, Eurotrib 85, Lion, (1985). 3. Ajder V, Poştaru A, Poştaru G, Ceban V,. 2009, Metodo-logical peculiarities of research on trybosystems with cyclic slip of piston-cylinder type. ModTech International Conference - New Face of TMCR. Iasi, Romania, 21-23th May. 4. Шустер Г., Детерминированный хаос. Введение. М.: Мир. (1988), 240 с. 5. В.Л. Заковоротный, Нгуен Донг Ань, Фам Динь Тунг. Устойчивость эволюционной траектории механической системы, взаимодействующей с трбосредой. Вестник ДГТУ, 2007. Т.7. №4(35) 6. Timashev S.F., Vstovsky G.V., Solovieva A.B., 2005, Informative essence of chaos, Unsolved problems of noise and fluctuations in physics, biology and high technology – UPoN. 7. Мусалимов В.М., Валетов В.А., 2006, Динамика фрикционного взаимодействия.- СПб: СПбГУ ИТМО, 191 с.

principles and methodological …...the fact that in the contact, processes of various origins...

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