RU2343450C2 - Frictional unit test technique - Google Patents

Abstract

FIELD: physics; testing.

SUBSTANCE: invention refers to mechanical frictional unit test techniques. Mechanical systems of object and model friction mechanical systems (FMS) consist of subsystems. Mechanical subsystems are described by combined similar linearised differential equations, while processes on frictional contact (FC) of "object" and "model" are described by similar mathematical models, regression equation received at natural experiment. Required "object" and "model" parameter ratio is provided. Triboparameters FMS are measured while testing. Friction factor is represented as complex function. It is accompanied with real time control and fixation of contact specific area. Contact temperature is defined by formula.

EFFECT: higher validation.

13 dwg

Description

The invention relates to methods for testing friction units of mechanical systems.

There is a method of determining operating conditions when testing friction units [1], which consists in registering high-frequency fluctuations of the forces of contact interaction in the friction unit and conducting a harmonic analysis of their spectrum of vibrations, from which the operating conditions of the friction unit are determined.

The disadvantage of this method is the lack of reliability of the results, which is due to the inability to take into account the influence of dynamic processes occurring in the mechanical system and on the friction contact of the friction unit, to ensure the identity of the conditions of the processes of friction and wear.

Closest to the described solution is a method for determining operating conditions [2] when testing friction units, which consists in the fact that the tests are carried out on a physical model with the necessary number of concentrated masses, ensuring equality of friction conditions, logarithmic damping decrements and vibration frequencies of the model and the unit, In this case, high-frequency oscillations of the forces of contact interaction in the friction unit are recorded and a harmonic analysis of their oscillation spectrum is carried out, the results of which determine the conditions of lation of the friction unit.

The disadvantage of the prototype method is the need to use concentrated masses, the placement of which at the necessary "points" in some cases causes a significant complication, and in many cases does not represent an opportunity, which entails insufficient reliability of the results. In addition, the measurement of microgeometry parameters of the friction surface when using the prototype method is performed at the end of the test, which, in turn, also leads to a decrease in the reliability of the results.

The technical task of the proposed solution is to increase the reliability of the results of determining operating conditions when testing friction units.

отношение времени протекания исследуемых процессов объекта (T) и модели (t) равно

отношение физико-механических параметров материалов (модуля упругости, температуры объемной и ее градиента и т.д.) объекта (Ф) и модели (ф) равно

отношение внешних сил, действующих внутри системы, объекта (F) и модели (f) равно

отношение площадей объекта (S) и модели (s) равно

при этом отношение амплитуд колебаний связей механических подсистем и деформаций микронеровностей объекта (А) и модели (a) равно

отношение параметров микрогеометрии фрикционных поверхностей объекта (Н) и модели (h) равно

отношение контактного давления объекта (Q) и модели (q) равно

отношение линейных скоростей скольжения объекта (V) и модели (ν) равно

отношение масс объекта (М) и модели (m) равно

отношение жесткостей объекта (С) и модели (с) равно

отношение частот колебаний объекта (Ω) и модели (ω) равно

отношение удельных величин спектральных плотностей мощности

- спектральная плотность сигнала x(f) в единицу времени Т на частоте Ω, приходящаяся на единицу площади S поверхности), при этом правые части дифференциальных уравнений (внешние возмущающие воздействия математических моделей ФМС) обеспечивают выполнение констант подобия амплитуды колебаний

и частоты колебаний

при этом измерение трибопараметров ФМС осуществляется во время проведения испытаний, коэффициент трения представляется в виде комплексной функции, т.е. в виде отношения взаимного трибоспектра в тангенциальном и нормальном направлениях к автотрибоспектру в нормальном направлении, действительная часть которого характеризует упругие, а мнимая - диссипативные свойства подсистемы фрикционного контакта, одновременно выполняется контроль и фиксирование удельной площади касания в реальном масштабе времени, например, методом проводимости в паре металл-металл или методом лазерного просвечивания в паре металл-полимер, а значение контактной температуры (максимальной объемной температуры, температуры на вершинах микронеровностей контакта) определяется формулой:The problem is achieved in that in the claimed method, the mechanical systems of the object and model friction mechanical systems (FMS) consist of a mechanical subsystem and a subsystem (friction) subsystem, while the mechanical subsystems are described by a system of similar linearized differential equations, and the processes occurring on the friction contact (FC) of the “object” and “model” are described by similar mathematical models, regression equations obtained in a full-scale experiment, for example, using m mathematical planning full or fractional factorial experiment, with between the parameters "object" and "model" is provided with the following relationship: the ratio of the linear dimensions of the object (L) and models (l) is equal to the geometric similarity scale

the ratio of the flow time of the studied processes of the object (T) and model (t) is

the ratio of physical and mechanical parameters of materials (elastic modulus, volumetric temperature and its gradient, etc.) of the object (Ф) and model (f) is equal to

the ratio of external forces acting inside the system, object (F) and model (f) is

the ratio of the areas of the object (S) and model (s) is

the ratio of the amplitudes of oscillations of the bonds of the mechanical subsystems and the deformations of the microroughness of the object (A) and model (a)

the ratio of the microgeometry parameters of the friction surfaces of the object (H) and the model (h) is

the ratio of the contact pressure of the object (Q) and model (q) is

the ratio of the linear sliding velocities of the object (V) and the model (ν) is

the mass ratio of the object (M) and model (m) is

the ratio of the stiffnesses of the object (C) and model (c) is

the ratio of the oscillation frequencies of the object (Ω) and the model (ω) is

ratio of specific values of power spectral densities

is the spectral density of the signal x (f) per unit time T at a frequency Ω per unit area S of the surface), while the right-hand sides of the differential equations (external disturbing effects of mathematical models of the FMS) ensure that the similarity constant

and oscillation frequencies

the measurement of the FMS triboparameters is carried out during the tests, the friction coefficient is presented as a complex function, i.e. in the form of the ratio of the mutual tribospectrum in the tangential and normal directions to the autotribospectrum in the normal direction, the real part of which characterizes the elastic and imaginary - dissipative properties of the friction contact subsystem, at the same time, the specific contact area is monitored and recorded in real time, for example, using the pair conductivity method metal-metal or by laser transmission in a metal-polymer pair, and the contact temperature (maximum volume temperature, perature in microroughness contact vertices) is defined by:

where J is the current passing through the contact,

R _to - contact resistance,

α _T is the coefficient of external heat transfer,

ρ is the resistivity

l _to - the "length" of the contact.

Let us consider the proposed method for testing friction units using the example of the FMS study "Rolling stock - track top structure" with the friction contact subsystem "wheel - rail". To study the dynamic properties of the electric locomotive and the track’s upper structure, we will use the VL80 electric locomotive with a design speed of up to 120 km / h, moving along the link junction path, as the most complex form of movement as a mobile unit.

According to the proposed method for testing friction units, modeling should consist of three stages.

1. The construction of a dynamic model of the mechanical subsystem of the object of study and the identification of the constants of the dynamic similarity of the mechanical subsystem.

2. Construction of a dynamic model of a subsystem or subsystems of frictional contact.

3. Building a model of the friction-mechanical system.

In the first part of the simulation, based on the analysis of differential equations of motion, similarity criteria for dynamic subsystems are derived. Despite the wide variety of existing machine designs, the dynamic qualities of any machine can be investigated by a general methodology, which is based on the laws of theoretical mechanics and oscillation theory. The condition for the dynamic equivalence of the initial and reduced systems is the equality of the kinetic and potential energies before and after the reduction. Consequently, the mass system of the calculated equivalent circuit of a mechanical system has a number of degrees of freedom equal to the selected number of masses of a real object, and its motion is described by the same number of equations. This makes it possible to solve the problem of modeling the main dynamic characteristics based on the method of analysis of differential equations of motion of the calculated equivalent circuit.

An electric locomotive can be imagined as a single mechanical system with many degrees of freedom, consisting of wheelsets, frames of bogies, a body and connections between these basic elements. The source of all dynamic disturbances in the path and rolling stock is a pair of wheels moving along uneven paths. The design of the wheelset and the devices placed on it greatly affects the course of all dynamic processes.

Oscillations of the wagons arise because the wheelsets, when moving along rails and turnouts, make complex spatial movements and thereby cause them to oscillate on the spring suspension of the trolley frame, body frame, bodywork and the track itself. Thus, the oscillations of the electric locomotive begin with a pair of wheels and are transmitted to all other friction units of the electric locomotive and the path. First of all, vertical vibrations of one wheel pair are considered.

Additional dynamic vertical forces transmitted by the wheel of the electric locomotive to the rail caused by vibrations of the overpressor structure must not exceed the body's static load on the wheel. If these forces reach values equal to the static load on the wheel (235 kN), then with the vibrations of the overpressor structure the same wheel unloading forces will arise, i.e. wheel derailment is possible.

Forces arising from the inertia of unpressed masses can reach several hundred kN. The causes of the inertia of the non-sprung masses are irregularities in the path and irregularities on the rolling surface of the wagon wheels. These bumps are divided into isolated and continuous, short and long. When a car moves along a link rail track connected at the joints by overlays, wheel collisions with rails always occur.

We introduce the following assumptions into the calculation scheme [3]. When studying the movement of an electric locomotive as a mechanical system interacting with the railway, the frames of the bogies and the body, regardless of their design, are most often considered as elements having only a certain mass (m) concentrated in the center of gravity of the element, and very rarely these elements are considered as structures having masses and stiffnesses distributed in space in a certain way [4]. We consider the body, trolley frames, and wheelsets to be absolutely rigid bodies. The average wheel diameters are the same. The path is uniformly elastic. An electric locomotive moves along a rail track with continuous vertical irregularities η that are identical for both rail threads (η ₁ = η '₁; η ₂ = η' ₂ , etc.). The real types of spring suspension, in addition to elastic deformations in the vertical direction, can elastically deform in the horizontal direction, but we will not do the estimated horizontal deformations of spring sets to simplify the solution of the problem. When bouncing, the body, wagon trolleys, and other masses make displacements parallel to the xOz plane. The stiffness due to compression of the metal in the contact of the wheel with the rail, compression of the wheel disk and the rail itself under the wheel (due to its local elastic deformations) will be presented in the form of the so-called "contact stiffness of the wheel and rail".

With this simplification, it is not necessary to take into account fluctuations in the wheel and rail, i.e. there will be no need to use partial differential equations needed to describe the elastic vibrations of colliding bodies [3].

We simplify the calculation scheme for solving our problem and present it in the form shown in Fig. 1, considering the vibrations of only one wheel.

In this case, the corresponding masses m _i , stiffness C _i and resistance coefficients β _{i are} reduced by the corresponding number of times.

Figure 1 shows the design scheme of the mechanical system "rolling stock - the upper structure of the track." We accept the following notation: m is the mass of the body of the electric locomotive, m _t is the mass of the sprung parts of the trolley, m _n is the mass of the non-sprung parts of the trolley (wheel pair), m _p is the reduced mass of the rail P65, m _w is the reduced mass of the sleepers, m _b is the reduced mass ballast; O, O _t , O _n , O _r , O _W , O _b - the corresponding centers of mass.

[4]; вертикальные жесткость и коэффициент сопротивления центрального подвешивания на тележку соответственно равны С и β; надбуксового подвешивания для колесной пары - 2С_m и 2β_m; массы обрессоренных и не обрессоренных частей тележки соответственно равны m_т и m_н. Для одного же колеса эти величины будут в 4 раза меньше, т.е.

Half of body weight is transferred to each trolley

[four]; the vertical stiffness and the coefficient of resistance of the central suspension on the trolley are respectively equal to C and β; over-wheel suspension for a pair of wheels - 2C _m and 2β _m ; the masses of the offended and not offended parts of the trolley are respectively m _t and m _n . For one wheel, these values will be 4 times smaller, i.e.

The external impact on the mechanical system is modeled by the unevenness of the rail on the modern link circuit of a standard design according to the formula proposed by VNIIZhT MPS N.N. Kudryavtsev [5]:

where A ₀ , B ₀ are the equivalent amplitudes of the roughness of the railway track,

A ₀ = 0.0077 m, B ₀ = 0.0047 m - for good condition of the path;

L _p is the length of the rail link, L _p = 25 m;

The system of differential equations of forced oscillations of the VL80 electric locomotive in the vertical plane with attenuation takes the following form:

where k _i are the circular eigenfrequencies of the oscillations of mass m _i on the elastic element with stiffness C _i , s; n _i - circular frequencies of damped oscillations, s ^-1 .

Since the processes in the original and model with dynamic similarity should be similar, they are described by the same differential equations.

In a first approximation, we assume that dissipative functions slightly affect the frequencies of natural vibrations, changing only the logarithmic decrement of vibrations, that is, when assessing the conditions of dynamic similarity, we will consider the mechanical system without friction, i.e. Ф = 0. (In the future, this assumption is eliminated by introducing the FC model into the FMS model, which ensures full compliance with the dynamic characteristics of the object and the FMS model.)

The structure of differential equations is the same, therefore, we consider only one of them, for example, the first row (1). We write down differential equations describing the motion of an object (o) and a model (m)

where m ₀ , m _m - body mass of the electric locomotive of the object and model; With _about , With _m - the stiffness coefficients of the cradle suspension of the object and model; z _o , z _m - linear dimensions of the object and model; Ω _o , Ω _m - natural (forced) vibration frequencies of the mechanical systems of the object and model.

Thus, the relations of all quantities characterizing them should be expressed using similarity scales:

where C _m - the scale of similarity of the mass; C _C is the scale of similarity of the stiffness coefficients; With _g - the scale of similarity of geometric dimensions; With _Ω - the scale of similarity of the oscillation frequency.

We introduce the obtained similarity scales in the differential equation (2) for the model, we obtain the following dependence

The identity condition of differential equations leads to the following similarity criteria:

из чего следует масштаб подобия времени испытаний, равный С_t=1.As a condition for dynamic similarity, we take the equality of the frequencies of the natural vibrations of the model and the object, that is, C _Ω = 1. Then we obtain from (4) the equality C _m = C _C for the translational type of motion. Subject to the specified conditions, we obtain the criteria

from which follows the similarity scale of the test time, equal to C _t = 1.

We will obtain similar equality conditions by considering three-, four-, ..., n - mass systems, that is, the adopted condition provides a dynamic similarity of the model and the object of mechanical systems for any n - mass system, including and for the mechanical system “rolling stock - the upper structure of the track”.

Based on the above analysis, we can conclude that to ensure the dynamic similarity of the simulated mechanical systems, it is necessary that, with the translational movement of mechanical systems, the similarity constants of the mass and linear stiffness of the system are equal to each other, i.e. With _m = C _C and with rotational motion - the equality of the similarity constants of the moment of inertia and the angular stiffness of the system, i.e. C _I = C _C. In this case, the model experiment should be carried out in real time With _t = 1, since, firstly, With _Ω = 1 and, accordingly, With _Ω = With _t = 1; secondly, when conducting FMS studies on physical models, we must produce model pairs from the same materials from which real friction surfaces are made. In this regard, the time intervals for the relaxation of the frictional contact bonds in real and model conditions are equal, which is ensured by the equality С _t = 1.

The second part analyzes the dynamic similarity of the friction contact subsystem of friction units.

At the frictional contact of the real friction units of mechanical systems, complex non-linear processes occur, depending on a large number of interrelated factors that form an inhomogeneous system of non-linear functional dependencies. The form of the differential equations of motion depends not only on what materials are used in the friction unit, at what loads and speeds they contact each other, what external control action is implemented in the system, but also in what mechanical system the friction unit functions. Theoretical dynamic calculation of FMS is a very time-consuming process, as it consists of tens and hundreds of degrees of freedom, with many assumptions, simplifications and linearization of dynamic processes. As a result of this, calculation results are often obtained that are inadequate to the actual operating conditions. An attempt to describe the dependence of the output characteristics of the FMS on the input factors, taking into account the properties of the contacting materials and the dynamic characteristics of the mechanical system, leads to a huge number of models (up to a million or more), which are ultimately impossible to study due to violation of the superposition principle for nonlinear systems. As a result of this, a large number of subsequent testing of friction units of real machines is required.

Thus, to carry out effective FMS optimization by theoretically calculated methods is a practically unsolvable problem. The most appropriate for the study of FMS optimization is the use of experimental and laboratory methods based on the technique of physical similarity and modeling [6 ... 13]. To solve the problems of complex FMS studies, to optimize their parameters on the basis of physical similarity and modeling methods, there are special techniques and stands for their implementation, which provide real operating conditions for machines and mechanisms with friction units.

A correct physical model of the FMS is more accessible for research than a real object. Moreover, some objects cannot be directly studied at all. If the model accurately reflects the behavior of the system, then it contains the necessary limitations, and this allows you to get a solution that reflects the state of the system that is possible for physical implementation.

The friction unit “wheel - rail” is an integral part of the FMS “rolling stock - track top structure”. The masses of the wheel m ₁ and the rail m ₂ make a complex mutual movement, are components of a mechanical system (figure 3). Figure 3 shows a model representation of the friction mechanical system "wheel-rail": F _T - the friction force; f is the coefficient of friction; F _H is the pressure; m ₁ is the mass of the wheel; m ₂ is the mass of the rail; σ is the heat transfer coefficient; λ is the thermal conductivity; α is the thermal diffusivity; h is the microroughness height; r is the radius of microroughness; θ is the contact temperature; τ is the ultimate shear stress.

In this case, the mutual contact surfaces represent a lower level system, the components of which are microroughnesses, which can be characterized by the mass of their active microvolume and the rigidity of the seal.

During frictional interaction of solids, complex mechanical and physicochemical processes occur on friction surfaces: oxidation, diffusion redistribution, phase and structural transformations, elastic and plastic deformation of microroughnesses, and destruction of surface layers. The higher the level of the subsystem, the less inertial are these processes. Due to the small spots of real contact, each contact exists for a short time. As indicated in / 14 /, for real rough bodies at an average relative displacement velocity of 1 m / s, the number of discrete contacts per unit time is estimated to be up to 100 kHz depending on the materials of the friction pairs, the average distance between microroughnesses, and the cleanliness class.

As a result of the mutual displacement of the contacting surfaces, the interaction of components (microroughnesses) at the frictional contact causes forced oscillations, which leads to the appearance of forced oscillations with the frequency of the disturbing force. Sliding friction is always accompanied by the occurrence of oscillations and heat generation / 15 /. By the active microvolume of the material of the friction surface, we mean that zone of deformation of the materials of the contacting bodies, in which processes develop that lead to a change in the physicomechanical properties of the materials of the contacting surfaces. That is, the active microvolume is that thin tribolayer that ultimately determines the tribological characteristics of friction pairs.

With vibrations of the active microvolumes of the material, deformations and stresses corresponding to them arise in themselves and in the layer surrounding them. The frequency of forced voltage fluctuations for a given active microvolume will be determined by the number of pulses of the interactions of the microvolumes per unit time. Normal and tangential stresses arising from the contact of microroughnesses will depend on coordinates, time, relative velocity and maximum volumetric temperature, since, in addition to these oscillations, active microvolumes of the material undergo fluctuations due to thermal peaks.

In the process of deformations of active microvolumes of FC masses, their sizes change, destruction, and the formation of new ones. In this case, the microroughnesses of the contacting surfaces will be formed and tend to occupy a position relative to each other so that energy losses during mutual over-deformation of the microroughnesses are minimally possible. Friction surfaces acquire the character of equilibrium roughness and are characterized by relatively stable geometric outlines of microroughnesses. A change in the reduced rigidity of the mechanical system (or the reduced moment of inertia) unambiguously leads to the transition process of friction, after which a new equilibrium roughness is established at the contact.

The process of forming equilibrium roughness on friction surfaces occurs when there is a resonance between the intrinsic carrier frequency of vibrations of active microvolumes, i.e., the frequency of vibrations of stresses on the contact surface caused by vibrations of active microvolumes and the frequency of vibrations of stresses corresponding to one of the natural frequencies of vibrations of the mechanical system. This stable state consists in the formation of one carrier frequency of the tribospectrum and its coincidence with the nth natural frequency of the mechanical system.

Thus, the total vibrational energy of the mechanical system is distributed over the spectrum of frequencies generated by it and, in relation to the microroughnesses of the contacting surfaces, represents the external force field of the voltage fluctuations in the tangential and normal directions. In the steady state operation of a mechanical system, the parameters of this force field are constant. The frequency spectrum of the forced vibrations of the active volumes of the friction contact material is very extensive, therefore, almost always it “covers” the frequency spectrum of the disturbing vibrations generated by the mechanical system.

Internal friction is one of the physicomechanical constants of the materials under study and is characterized by dimensionless coefficients (absorption coefficient, mechanical Q factor, logarithmic decrement of vibrations), that is, it does not depend on the geometric dimensions of bodies, and therefore on the geometric scale in physical modeling.

The value of the coefficient of friction depends on the sliding speed, since the conditions of interaction and destruction of surfaces change. The generally accepted pattern of change in the coefficient of friction as a function of the sliding velocity in the form of a falling characteristic changes significantly at high sliding velocities, since this causes significant heat generation. The sliding speed determines the number of interacting microroughnesses per unit time, that is, the frequency of the forced vibrations should be proportional to the sliding speed. Therefore, a change in the sliding speed and, as a consequence, the frequency of the forced vibrations will lead to a change in the existing equilibrium state (resonance) between the natural vibration frequency of active microvolumes and the forced vibration frequency. The transition of the system to a new stable state will be associated with a change in the topography of the friction surfaces until equilibrium roughness is established at a different resonance level. Thus, in order to ensure the adequacy of the friction processes in the model and nature, it is necessary to ensure equality of the similarity constants for the speed of the relative motion of the contacting surfaces - With _Vsk = 1.

Between the sliding velocity and the temperature of the surface layer, ceteris paribus, there is a dependence: according to the Eger formula / 16 /, the temperature is proportional to the root of the sliding velocity. At a temperature of 100 ... 200 ° C due to the discrete nature of the contact, the proportion of plastic contact in the total stress-strain state of the surface increases and the contact pressure decreases. The melting of the surfaces of the active microvolume of the mass of the friction surface leads to a change in their shape, which in the general case is accompanied by an increase in the actual contact area and a proportional decrease in contact pressures. At the same time, the friction temperature does not change from this, i.e. the temperature gradient is independent of pressure and is completely determined by the sliding velocity. Temperature peaks are almost completely realized in the active microvolume. Even at a contact temperature of 800 ... 1000 ° C, the volumetric temperature of the rest of the material will slightly differ from the surrounding 30 ... 60 ° C / 17 /. This suggests a very intense temperature gradient of the active microvolume. The duration of the temperature peak and the period of transition from heating to cooling and vice versa is 0.1 ... 1.0 ms / 18 /. This allows temperature peaks to be characterized as parameters having a frequency and amplitude.

The magnitude of the active microvolume depends on the physicomechanical characteristics of the contacting surfaces, as well as on the parameter PV (product of the relative sliding velocity and pressure) and is limited by the depth at which the effect of temperature on the physicomechanical properties of materials of rubbing bodies is tangible.

The main criterion for the reliability of a model experiment can be considered the implementation under the conditions of the model of the same type of wear of the surface layers and the wear rate of the contacting bodies, which is the main one for real friction surfaces. The analysis shows that to ensure the conditions of dynamic similarity of processes on the surface of the frictional contact when modeling friction conditions, the following conditions must be met:

- the researcher has the right to choose the geometric scale of the model C _g and proportionally change, for example, the nominal contact area A, i.e. With _A = C _g ² , the length of the friction path C _L (C _L = 1), the radius of curvature r ₁ or r _{2 of the} wheel and rail (C _r = C _g ), the diameter of the skating circle d (C _d = C _g ). However, it is impossible to apply the scale factor C _g to the geometric parameters that determine the linear dimensions on the area of actual contact (micro-roughness);

- sliding speeds, i.e. With _Vsk = 1;

- if the contact modes during model and full-scale tests are the same, then the roughness parameters for the steady-state friction mode will be the same, and their similarity constants, for example, for the microroughness height С _h , the radius of curvature of microroughness С _r should be equal to one (С _r = 1, С _h = 1). This contradicts the accepted similarity constant of linear dimensions, since the reduced parameters of unit microroughness h and r are linear dimensions, and С _l ≠ 1. Forced change in roughness in accordance with C _l , as is customary in Brown E.D. / 19 /, with constant contact pressure and sliding velocity parameters for the model and the real friction unit, that is, C _q = 1, C _Vsk = 1, creates an unsteady friction mode ( _running- in process) on the surface, which, after completion and reaching the steady state friction leads to the implementation of equilibrium roughness with _r = 1, _h = 1;

С учетом полученного из условий динамического подобия условия равенства скоростей скольжения и параметров шероховатости для модели и натуры равенство контактных давлений обеспечивает реализацию на поверхности трения для модельного эксперимента характерного для реальной поверхности вида изнашивания;- the process of changing geometric parameters continues until the contact pressure q is equalized on the spots of actual contact. This allows us to characterize the contact pressure on the friction surface as a criterion whose equality for the real friction surface and the model is decisive, i.e.

Taking into account the conditions of equality of sliding speeds and roughness parameters for the model and nature, obtained from the conditions of dynamic similarity, the equality of contact pressures ensures that the wear type characteristic of a real surface is realized on the friction surface for a model experiment;

- to maintain the equality of contact pressures at the contact, the normal load on the contact should have a scale factor of transition from nature to the model, equal to the scale factor of the contact area, that is, С _N = C _S = С _l ² ;

во-вторых масса прямо пропорциональна силе трения

где g - ускорение свободного падения (С_g=1), т.е. масштабный фактор массы имеет размерность силы

- equality of contact pressures for the object and model, i.e. With _q = 1, determines the equality of the scale factor of mass С _m = С _l ² , since, firstly, the contact pressure is directly proportional to the force and inversely proportional to the contact area

secondly, the mass is directly proportional to the friction force

where g is the acceleration of gravity (C _g = 1), i.e. the scale factor of mass has the dimension of force

- under identical conditions at the contact for the model and the real surface, equal proximity correspond to equal friction coefficients f and equal specific linear wear i _h .

- natural and characteristic natural vibration frequencies (which should be considered as a physicomechanical characteristic of the friction surface under the steady-state friction regime, and in order to preserve the equality of the characteristic frequencies of natural vibration, the condition for equality of the similarity constants of the embedment stiffness and the moment of inertia of the active microvoltage of the friction material contact relative to its center of oscillation, that is, C _C = C _I );

- the magnitudes of the strain amplitudes of the contacting micro-, macro-roughnesses of the frictional contact and the bonds of mechanical systems during model and field tests are equal to unity C _A = 1, where A is the amplitude of the bond vibrations and the roughness value.

- the process of frictional contacting should be implemented in real time, that is, With _t = 1.

At the third stage of modeling, the criteria of physical similarity of the friction unit of the friction-mechanical system are considered.

The friction unit is a subsystem of the friction mechanical system; in addition, it cannot be considered as a subsystem of one level. For example, when considering such friction units as the “sleeve-clutch” shown in FIG. 3, the system is the crew on the way, the subsystem is the FMS “wheel-lubrication-rail” (structural components). Second-order subsystems (or subsystem elements) are parameters that characterize the properties of friction surfaces, friction, and wear. As a criterion for assessing the functioning of the system, we can take the wear rate of surfaces I.

In the design of the system under consideration, one can distinguish the loading mechanism, the leading and driven parts, connected by the stiffness of the connections with the mechanical drive system of the machine, the system of damping elements of the friction unit, etc. The marked structural elements of the friction unit constitute its mechanical part, the sublevel of which are directly the contact surfaces.

Therefore, when developing a structural model of a complex process (for example, locomotive braking) in / 20 /, the model is divided into several steps - groups of the 1st order subsystem, each of which is divided into 2nd order subsystems, etc. Accordingly, a graphical representation of the physical model of the friction unit (figure 3). If in the subsystem of the mechanical part of the friction unit (Fig.3.a) the mode parameters (speed, load), heat transfer surfaces and heat absorption volumes, shape parameters (mass, stiffness, moments of inertia, hardness, etc.) are formed, then in the subsystem friction surface (Fig.3.b) the contact microgeometry parameters are formed (height and radius of the active microvolume, the proximity of the contacting surfaces), the average volumetric temperature of the friction contact and the contact temperature, the stress-strain state of the active microvolume s, amplitude-phase-frequency characteristics (AFC) of internal friction processes.

Evaluation of the dependence of the tribological parameters of the friction unit on the parameters of loading, modification of the friction surface, temperature, and environmental influences allows us to confine ourselves to the first-order subsystem, the parameter estimates of which are presented in Figures 3.a and 3.b.

Using these models (figure 4) of the processes of friction and wear of the friction node "wheel-rail", we present in general terms the functional dependence of the process:

where σ ₁₂ is the heat transfer coefficient, W / (K · m ² ); N - normal wheel load on the rail, N; V is the rolling speed, m / s; C is the linear stiffness of bonds, N / m; k is the frequency of natural oscillations, s ^-1 ; q is the pressure in contact, Pa; ΔΘ - temperature gradient, K / m; J is the moment of inertia, kg · m ² ; β — viscous damping, (N · s) / m; HB - hardness of materials, Pa; E is the modulus of elasticity, Pa; τ is the friction time, s; L is the friction path, m; S is the contact area, m ² ; F is the friction force, N; U - weight wear, kg / m ³ ; C is the coefficient of specific heat, J / (kg · K); And - the amplitude of the deformation of bonds, m

At the stage of modeling the mechanical, thermal and dynamic similarity of the entire mechanical system, it is necessary to take into account the constraints that determine the dynamics of a mechanical system without friction and the conditions that determine it, and the identity of similar physical processes occurring at the frictional contact of the model and the object.

For this, when using the dimensional analysis method (with restrictions / 15 /), stiffness C as the main variable is introduced into the number of basic parameters, and time τ and contact pressure q are introduced into the boundary conditions.

In the MLT основных basic unit system (mass, length, time and temperature), we select four basic parameters that have the most significant effect on the friction and wear of the friction system and can be measured in laboratory tests:

The system of equations formed by four basic parameters has the form:

lnσ = lnM + 0 · lnL-3 · lnT-lnΘ;

lnN = lnM + lnL-2-lnT + 0 lnΘ;

lnV = 0 · lnM + lnL-lnT + 0 · lnΘ;

lnC = lnM + 0 lnL-2 lnT + 0 lnΘ.

The main determinant D _{0 of the} system of equations in numerical form, formed by the parameters MLTΘ:

The determinant D ₀ ≠ 0, which confirms the independence of the parameters σ, N, V, C. chosen as the base dimensions.

As the boundary conditions, we choose the oscillation frequency, contact pressure, and temperature gradient, i.e., C _k = 1, C _q = 1, C _ΔΘ = 1, which is achieved by using the same parameters of nature and model.

The calculation of scale transition coefficients (MCP) for the adopted model and nature relative to a given scale coefficient of circular stiffness C _{C is} carried out according to a program that implements an algorithm for solving linear equations with n unknowns. The calculation results are summarized in table 1.

As an example, we present the derivation of the similarity criterion for a nonbasis parameter of the temperature gradient in matrix form, after which we will verify the result.

Using the main determinant of the system D ₀ , we combine each parameter with the base σ, N, V, C. For this, we replace the rows with the parameters σ, N, V, C with the rows with the dimensions of the parameter for which the similarity criterion is determined. For each parameter, we obtain four determinants, after which we derive similarity criteria.

The temperature gradient criterion [ΔΘ] = [M ⁰ L ^-1 T ⁰ Θ ¹ ].

Calculation of determinants:

будет иметь вид:Similarity criterion for temperature gradient parameter

will look like:

или

тогда

or

then

Verification:

The criterion for the amplitude of bond deformation [A] = [M ⁰ L ¹ T ⁰ Θ ⁰ ].

The similarity criterion for the parameter of the amplitude of deformation of bonds A will have the form:

или

тогда

or

then

что подтверждает неизменяемость микрогеометрии поверхностей при модельных и натурных исследованиях.Verification:

which confirms the immutability of surface microgeometry in model and field studies.

In a similar way, all other parameters of the friction process adopted for modeling are associated with the basic parameters.

The similarity equation, combining the obtained criteria, consists of 14 criteria, since according to the Buckingham theorem it should be equal to the number of parameters minus four basic:

The obtained similarity criteria that make up the criterion equation (6) require experimental verification. This is due to the fact that they can have completely limited application boundaries. In addition to experimental verification, one can compare the obtained criteria with the “standard” ones, which have been repeatedly tested in studies of the processes of friction and wear, as well as in other areas of technology.

The criteria (see table 1) are obtained as the dependences of the modeled value on the parameters taken as basic, that is, on the values that have the greatest impact on the process under study. Accordingly, a change in the basic parameters will also change the resulting criteria. However, as practice shows, such changes do not affect the implementation of “standard” criteria if the selection of basic parameters and modeling are carried out correctly.

Consider several heterogeneous "standard" criteria characterizing the ratio of power, thermophysical processes and the processes of lubrication on the friction surface:

где V - скорость, τ - время, L - путь, в реализованном моделировании получается, если критерий времени π_τ разделить на критерий пути трения π_L, то есть

Так как в выражение критерия гомохронности входят параметры V, τ, L, то даже если ни один из этих параметров не входит в число базисных, перемножение критериев скорости и времени и деление на критерий пути в результате обеспечивает получение критерия гомохронности.1. The criterion of homochronism, characterizing the homogeneity of processes in time:

where V is the velocity, τ is the time, L is the path, in the implemented simulation it turns out if the time criterion π _{τ is} divided by the friction path criterion π _L , i.e.

Since the parameters V, τ, L are included in the expression of the homochronism criterion, even if none of these parameters is included in the basic ones, multiplying the criteria of speed and time and dividing by the criterion of the path as a result provides a criterion for homochronism.

то есть

2. We obtain Newton’s criterion if we multiply the friction force criterion π _F by the time criterion π _τ , divide by the mass criterion π _m and substitute the value

i.e

3. We obtain the Froude criterion if we divide the mass criterion π _m by the time criterion π _t with the subsequent substitution N = mg and

умножив на квадрат критерия гомохронности, получаем

multiplying by the square of the criterion of homochronism, we obtain

4. We obtain the Fourier criterion if we divide the thermal diffusivity criterion π _Θl by the friction path criterion π _L with subsequent substitution

5. The Nusselt criterion can be obtained if the criterion of the path π _{L is} divided by the criterion of thermal conductivity π _λ :

Thus, the performed calculations make it possible to determine the scale factors of the transition from the object of study to the model experiment, perform bench tests and transfer the test results to the object of study.

On the basis of physical and mathematical modeling, two experimental stands were made to study the dynamic properties of the entire mechanical system as a whole and the individual wheel-rail FC.

To carry out a complex of model tests to assess the dynamic properties of the rolling stock and the track superstructure (VSP), the effect of the modification of the friction surface of the wheel-rail pair, as well as the VSP damping value on the magnitude and stability of the adhesion coefficient values, a test bench is presented, shown in FIG. 5.

The design of the stand allows comparative tests on crew models on a stand simulating a railway track and its impact on the running gear of the rolling stock (bouncing, galloping and side-rolling). The test bench is a frame 2 made of channels, on which a DC motor 3 is mounted (for modeling the resistance to movement of rolling stock) and bearing bearings 4. On the consoles of the shafts of the track rollers 5 are bevel gears connected by cardan shafts to an electric motor 3. On Track rollers of the 5th stand are installed crew model. The position of the wheels of the model relative to the support rollers of the bench is adjusted by the screws 6 installed in the support 1. Asynchronous motors are installed on each wheel pair.

The design of the stand allows you to test biaxial and four-axle crews, vary the distance between the axes of the rollers of the stand depending on the base of the carts. The crew model tested at the stand presents a copy of its running gear, in which the rigidity of the joints, the moments of inertia and the mass distribution along the axles of the wheelsets are respected. Track rollers of the stand have a design that allows you to simulate the main types of crew vibrations. Under the influence of the gravity of the rolling stock, the rail is subjected to deformations, the magnitude of which depends on the rigidity of the rail base and the rigidity of the rail itself. In order to simulate the processes of interaction of the rolling stock with the rail track, the track structure is simulated by the track rollers.

The roller of the stand, modeling the rail (Fig.6), is made of the same material as the railway rails. Two consoles are formed in the roller to simulate the rail junction, while the length of the console and the moment of cross-section resistance A-A models the compliance of the rail junction.

The rigidity and flexibility of the rail base is modeled by installing the support 2 of the shaft 1 of the stand on the layered structure of the lining 3 (Fig.7). The eccentricity of the rollers is created by shifting the axis of the track rollers 4 of the stand (figure 5) relative to the axis of the shaft 1 and securing them with a design bar 5.

On Fig presents photographs of the modernized roller stand.

Technical characteristics of the stand:

The frequency of rotation of the track rollers, rpm - 0 ... 500

The diameter of the track roller, m - 0.5

Gauge, m - 0,304

Modeled path frequencies and amplitudes:

- in the vertical plane - 6 ... 30 Hz, 3 ... 7 mm;

- lateral pitching - 1.5 ... 10 Hz, 3 ... 7 mm

Maximum eccentricity of road wheels, mm - 20

Single axle load, kN - 1.52 ... 2.4

The mass of non-sprung parts of the wheel-motor block, kN - 0.24 ... 0.48

The mass of the cart, kN - 0,64 ... 2

The mass of the offended part of the crew, kN - 4.8 ... 9.6

The measuring complex system consists of an IBM / PC type PC, multi-channel vibration sensor amplifiers with synchronization channels, a strain gauge signal amplifier, a digital signal processing board with a 9-channel analog-to-digital converter (ADC), connecting cables, a power supply, and a specialized software package.

The experimental determination of the traction characteristics realized on the bench when rolling the wheel model according to the VSP model is performed using strain gauges (Fig. 8.d). The coefficient of adhesion is estimated by recording the traction force from the load cells T ₁ and T ₂ located on the coupling ring of the stand, with a preliminary calibration Δ = f (P), where P is the applied force, Δ is the strain value. The experimental determination of the dynamics parameters realized at the bench when rolling the wheel model according to the VSP model is carried out using D14 vibration sensors.

To study the dynamic, tribotechnical and tribospectral characteristics of the friction subsystem “wheel-rail” of the friction mechanical system “track-rolling stock” on a discrete set of frequencies and to establish the values of the wear rate characterizing the durability of the joints, a new setup was implemented that implements reciprocating motion. The installation diagram is presented in figures 9 and 10. (Figure 9 shows the kinematic installation of reciprocating friction of the laboratory complex "path-rolling stock": 1 - electric motor; 2 - belt drive; 3 - pulley; 4 - backstage; 5 - specimen fixing device; 6 - upper counter-sample (wheel); 7 - lower sample; 8 - friction force strain gauge; 9 - sample holder; 10 - trolley; 11 - loading device in the horizontal direction; 12 - axis of the upper counter-sample; 13 - loading device in normal direction; 14 - normal force strain gauge nom direction 15 -. biasing the lever 10 is a picture of the general form installation).

The drive of the complex consists of an electric motor with asynchronous control and belt drive, which allows to carry out the specified relative sliding speeds of the friction pair under study during the working stroke of the reciprocating motion of the lower sample 7 L = 100 mm, which corresponds to the specified frequency of mutual displacement and fluctuations of the wheel-rail FMS . The predetermined frequency of the mutual movement is carried out by changing the eccentricity of the wings 4, i.e. the mounting points of the wings 4 on the pulley 3. Normal pressure on the contact is created by calculating the corresponding area of the tested samples. Registration of the obtained spectrum of vibrations of the tribocouple is carried out by strain gauges 8 and 14. Data from the sensors through the strain gauge is transmitted to a computer, where they are graphically interpreted.

When the drive is turned on, the crank 4 rotates and the lower sample 7 is reversed relative to the upper 6. Due to the friction force arising in the contact, the upper sample rotates relative to the lower sample relative to the fixed axis 12 of the studied threaded connection. The signal excited by the studied frictional interaction is recorded by strain gauges that operate in the frequency range determined by the program parameters of the Friction Mechanical System laboratory complex, in which the lower frequency is 0 Hz and the upper frequency is 40 kHz (according to the technical characteristics of the analog-digital converter). The vibrations of the loading device 13 are recorded in the normal direction of the friction force and the tangential direction by the device 11. For processing the experimental data, the MATLAB program was used, supplemented by a software module that allows solving the problems of tribo-frequency adaptation, which allows determining the autospectra of the normal and tangential forces separately, the mutual spectrum, and the frequency transfer function and other characteristics of vibrations of the studied tribopairs.

So, for example, when moving from a six-mass dynamic system (Fig. 1) to a three-mass model of frictional contact on a discrete set of frequencies, based on the equality of the kinetic and potential energies and the selected scale factor, the values of the masses and bond stiffnesses are reduced as follows

where m _1pr - the mass of the body and the sprung part of the trolley are given to the mass of the loading arm 15; m _2pr - the mass of the wheelset is reduced to the mass of the upper counter-sample 6 (wheel); m _3pr - the mass of the rail, sleepers and ballast are given to the mass of the lower sample 7; With _1pr - the stiffness of the cradle and spring suspensions are reduced to the simulated stiffness of the spring 13; With _2pr - the contact stiffness of the wheel and rail is investigated by the method of actual contact area; With _3pr - the stiffness of the rail, sleepers and ballast are reduced to the rigidity of the trolley 10.

Then the system of differential equations (1) takes the following form

To determine the natural frequencies of vibrations of such a mechanical system, we choose the external effect η in the form of η = η ₀ · sin (ω t) on the mechanical system. Then the mass expressions will be the following expressions

where a _i are the amplitudes of mass displacements.

After substituting the functions in equations (8), we obtain

Despite the fact that in equations (9) there are four unknowns (amplitudes and frequency), the frequency can be calculated as follows.

и такие же отношения из второго уравненияFrom the first and third equations (9) we find the ratio of the amplitudes of the oscillations

and the same relationship from the second equation

The compatibility of the obtained expressions leads to an equation in which one unknown is the frequency ω:

or

Having solved the obtained system of equations with respect to the unknown frequency ω, we can find the unknown values of the oscillation amplitudes, substituting the frequency values in (10).

The software of the test benches includes a special program for recording and processing signals from the sensors of the roller stand and the “Actual Touch Area” vibro installation. A screenshot of the program is presented in Fig. 11.

The program sets:

- sampling rate - the maximum frequency depends on the clock frequency of the computer, the technical characteristics of the ADC and is selected experimentally (for example, 40 kHz);

- sampling duration - sets the recording time in seconds. Recording starts from the moment you press the START key and continues until the time specified in this paragraph expires or until you press the STOP key. The recording time is limited only by the size of the computer's hard drive;

- calibration - the levels that are currently set are considered zero (a zero offset is selected).

The signals recorded by the program are used by a signal processing program, for example MATLAB. MATLAB system developed by The MathWorks, Inc. (USA, Neytik, Massachusetts) and is an interactive system for performing engineering and scientific calculations, focused on working with data arrays. The system uses a mathematical coprocessor and allows access to programs written in FORTRAN, C and C ++.

The software calculates the frequency transfer function based on the results of processing the normal load and friction force signals and, based on the analysis of the frequency transfer function, the FMS dynamic state is analyzed and its stability is checked according to the stability criteria of Nyquist, Lyapunov, etc.

We give some theoretical information / 21 ... 23 /.

Let the output signal of the friction node y (k) represent the sum (with weight coefficients) of a certain number of previous output samples, depending on a number of input samples u (k) (including the last). If we group the obtained terms in such a way that there are only input samples on the one side of the equal sign, and only the weekend on the other, then we get a notation form called the difference equation:

where k is the reference number, a _j , b _i are real coefficients.

The structure of the difference equation is similar to the structure of the differential equation of the analog system, but instead of the differentiation operation, the delays of the discrete signal sequences appear in the formula.

The output signal, based on the linearity and stationarity of the system in question, should be a linear combination of impulse characteristics:

where w (k) is the impulse response of a discrete dynamic system.

A convenient way to analyze discrete sequences is by z-transform. Its meaning is that the sequence of numbers {u (k)} is associated with the function of the complex variable z

where z ^-k is a discrete filter memory element delaying a discrete sequence by k clock cycles (z ^-k = e ^-pT ); u (k) - samples of the input signal; U (z) is the z-transform of the input signal.

Knowing the impulse response of a discrete system allows you to analyze the passage through a discrete system of any signal and find the internal state of any dynamic system. Applying the z-transformation to the equations of the discrete system (12), we obtain the system function of the discrete system or the transfer function (transfer function)

where Y (z) and U (z) are the z-transforms of the output and input signals; w (k) is the impulse response of the system from the kth sample of the input signal.

Applying the z-transformation to both sides of the difference equation (11), we obtain

From here it is easy to obtain the form of the transfer function of a discrete system:

Thus, the transfer function of a physically feasible discrete system shows how the complex amplitude of a sinusoid with frequency ω changes as it passes through the system and can be represented as the ratio of polynomials in negative powers of the variable z. The numerator polynomial characterizes the external impact on the friction unit, and the denominator polynomial (characteristic polynomial) is the result of this effect on the friction unit.

) входного и выходного сигналов, дальше рассчитывается взаимный спектр входного и выходного сигналов, представляющий собой произведение их спектральных функций, одна из которых подвергнута комплексному сопряжению:Knowing the spectra * (* Spectrum is a representation of the analyzed signal not in the time domain of the study, but in the frequency domain. The signal is converted from the temporary domain of research into the frequency domain by the fast Fourier transform algorithm according to the expression

) of the input and output signals, then the mutual spectrum of the input and output signals is calculated, which is a product of their spectral functions, one of which is subjected to complex conjugation:

- комплексное сопряжение спектральной плотности входного сигнала. Если сигнал u(t-τ) - четная функция, то спектр будет чисто вещественным (будет являться четной функцией). Если u(t-τ) - функция нечетная, то спектральная функция

будет чисто мнимой (и нечетной);

- энергетический спектр входного сигнала, автоспектр; W(ω) - комплексный коэффициент передачи системы; u(t) - входной сигнал, поступающий на узел трения (изменение нормальной нагрузки), Н; у(t) - выходной сигнал, полученный в результате трения (тангенциальная сила трения), Н; t - регистрируемое время, с; τ - временной сдвиг выходного сигнала относительно входного, с ω - регистрируемая частота сигналов

, Гц; f_д - частота дискретизации АЦП.Where

- complex conjugation of the spectral density of the input signal. If the signal u (t-τ) is an even function, then the spectrum will be purely real (it will be an even function). If u (t-τ) is an odd function, then the spectral function

will be purely imaginary (and odd);

- energy spectrum of the input signal, auto-spectrum; W (ω) is the complex transmission coefficient of the system; u (t) is the input signal supplied to the friction unit (change in normal load), N; y (t) is the output signal resulting from friction (tangential friction force), N; t is the recorded time, s; τ is the time shift of the output signal relative to the input, with ω is the recorded frequency of the signals

Hz; f _d - sampling frequency of the ADC.

Thus, if the spectra of the signals do not overlap, then their mutual spectrum is equal to zero at all frequencies and the mutual correlation function of these signals will also be equal to zero for any time shifts τ. Therefore, signals with non-overlapping spectra are uncorrelated.

From the obtained expression (16), the complex transmission coefficient of the discrete system is determined

The mathematical models of the dynamics of real technical systems are mainly non-linear and in many cases cannot be linearized due to the possibility of losing the characteristic dynamic properties due to the fundamental non-linearity of the equations of dynamics. However, with some limitations, the frequency transfer function of the mechanical system is linearized by the criterion of the minimum dispersion of the output signal of the Dirac impulse function / 24 /. The optimal order of the polynomials of the numerator and denominator is the order of the polynomials of the numerator (m) and the denominator (n) of the transfer function (11), in which the dispersion of the output pulse signal will be minimal.

The result of the analysis of amplitude-phase-frequency characteristics (AFC) is the ability to check the stability of the internal space of the system states and the value of the complex coefficient of friction acting in the friction zone of the tested samples / 25, 26 /:

where A (ω) = | f (iω) | - amplitude-frequency characteristic of the coefficient of friction; ψ (ω) = argf (iω) is the phase-frequency characteristic of the friction coefficient; U (ω) = Ref (iω) is the real frequency characteristic of the friction coefficient; V (ω) = Imf (iω) is the imaginary frequency response of the friction coefficient.

A fragment of the program in the programming language MATLAB is given in Appendix 1.

Consider the process of changing the coefficient of adhesion of the wheels of locomotives with the rail in time (Fig).

и масштабном факторе нормальной нагрузки С_N=C² _l=576) и скорости качения колес модели V_м=0,1 м/с и объекта исследования V_o=2,4 м/с=8,64 км/ч. Результаты приведены на фиг.13, соответствующие трению качения колеса по рельсу (фиг.12.а), трению качения с проскальзыванием (фиг.12.б) и чистому скольжению колеса по рельсу (фиг.12.в).The study of this dynamic process will be performed on the installation “Actual contact area” at normal load N _m = 0.408 kN (static wheel load on the rail N _o = 235 kN, with respect to the linear dimensions of the wheels of the locomotive

and the scale factor of the normal load ( _N = C ² _l = 576) and the rolling speed of the model wheels V _m = 0.1 m / s and the object of study V _o = 2.4 m / s = 8.64 km / h. The results are shown in Fig.13, corresponding to the rolling friction of the wheel along the rail (Fig.12.a), rolling friction with slipping (Fig.12.b) and the clean sliding of the wheel along the rail (Fig.12.c).

Using this technique, it is possible to predict the moment of friction disengagement in the form of the Nyquist hodograph, which characterizes the redistribution of the dissipative and conservative components of the frictional interaction energy of the analyzed tribosystem. At high values (ψ> 0.25) of the adhesion coefficient (Fig.13.a), the relative slippage is negligible and, as a result, the main part of the Nyquist curve is located in the high-frequency region. Before the clutch breaks down, the conservative and dissipative components of the energy are redistributed towards the latter. The increase in the dissipative component causes the "stretching" of the Nyquist hodograph along the imaginary axis (Fig.13.b) more than 30%. Disruption of adhesion (Fig.13.v) is characterized by instant redistribution of the work of friction forces.

Based on the obtained methodology, a system was developed for predicting the breakdown of the adhesion of a wheel to a rail based on an analysis of the correlation between the active and reactive moments on the axles of the wheelsets with subsequent action on the power drives and feed drives of the clutch activator (friction modifier).

Claims (1)

A method of testing friction units, in which the mechanical systems of the object and model frictional mechanical systems (FMS), consisting of a mechanical subsystem and a subsystem or friction subsystems, while the mechanical subsystems are described by a system of similar linearized differential equations, and the processes occurring on the friction contact (FC) “Objects” and “models” are described by similar mathematical models, regression equations obtained in a full-scale experiment, for example, using mathematical th scheduling full or fractional factorial experiment, with between the parameters "object" and "model" is provided with the following relationship: the ratio of the linear dimensions of the object (L) and models (l) is equal to the geometric similarity scale

the ratio of the flow time of the investigated processes of the object (T) and model (t) is

the ratio of physical and mechanical parameters of materials (elastic modulus, volumetric temperature and its gradient, etc.) of the object (Ф) and model (f) is equal to

the ratio of external forces acting inside the system, object (F) and model (f) is

the ratio of the areas of the object (S) and model (s) is

characterized in that the ratio of the amplitudes of the oscillations of the bonds of the mechanical subsystems and the deformations of the microroughness of the object (A) and model (a) is equal to

the ratio of the microgeometry parameters of the friction surfaces of the object (H) and the model (h) is

the ratio of the contact pressure of the object (Q) and model (q) is

the ratio of the linear sliding velocities of the object (V) and the model (ν) is

the mass ratio of the object (M) and model (m) is

the ratio of the stiffnesses of the object (C) and model (c) is

the ratio of the oscillation frequencies of the object (Ω) and the model (ω) is

ratio of specific values of power spectral densities

- the spectral density of the signal x (t) per unit time T at a frequency Ω per unit area S of the surface), while the right-hand sides of the differential equations (external disturbing effects of mathematical models of the FMS) ensure that the similarity constant

and oscillation frequencies

the measurement of the FMS triboparameters is carried out during the tests, the friction coefficient is presented as a complex function, i.e. in the form of the ratio of the mutual tribospectrum in the tangential and normal directions to the autotribospectrum in the normal direction, the real part of which characterizes the elastic and imaginary - dissipative properties of the friction contact subsystem, at the same time, the specific contact area is monitored and recorded in real time, for example, using the pair conductivity method metal-metal or by laser transmission in a metal-polymer pair, and the contact temperature (maximum volume temperature, perature microroughness on the tops of pins) defined by the formula

where J is the current passing through the contact;
R _to - contact resistance;
α _T is the coefficient of external heat transfer;
ρ is the resistivity
l _K is the “length” of the contact.

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