Analytical evaluation of materials wear resistance and tribotechnical coupling resource

When predicting the durability of various friction units at the design stage of the machine, an experimental-analytical standard of wear resistance is used. Its definition requires long-term and expensive experimental studies of samples or full-scale analogs. In order to reduce these costs, in this work, the fundamental theoretical dependences are derived for evaluating the wear resistance and the life of tribocoupling operating in stationary conditions of friction and fatigue wear. The basis for building the desired dependencies is a thermodynamic analysis of the steady-state process of friction, as a dual, molecular-mechanical process. The verification of the obtained theoretical dependences was carried out by comparing the calculated and experimental values of the wear resistance of samples abraded by the FCM-1 friction commercial machine according to the standard “steel roller - cast iron pad” under various conditions of friction interaction. The obtained results showed a fairly high adequacy of analytical dependencies. The proposed equations can be used to calculate the expected life of various tribocoupling at the design development stage of machines or their reconstruction.


Research target setting
Traditionally, the tribocoupling resource at the design stage of a machine is determined by the criteria of their wear resistance [1 -4]. According to GOST 23.001 and GOST 27.674 [5,6], the coupling wear resistance, as a property of triboelements materials resisting wear in certain friction conditions, is evaluated by a semi-empirical indicator: where t ск L V t = ⋅ -the calculated relative slip path of the triboelements being worn over the surface of the solid counter body associated with it at a rate ск V in time t ; 1 2 y y t y y = ⋅ = +  -measured linear wear over time t with average speed y  ; However, the need for long-term and expensive experiments, in determining this indicator, leads to the problem of estimating the design life of a machine because of the large number of studied tribocouplings that limit its durability. In order to solve this problem, this paper proposes the method for analytic design assessment of wear resistance and coupling life without conducting experimental studies.

The derivation of the basic equations for the design assessment of tribocoupling durability and resource
In order to simplify the mathematical calculations, we will consider stationary coupling operating under steady-state temperature and force conditions of friction and fatigue wear.
The basis for building the desired dependencies is a thermodynamic analysis of the steady-state process of friction, as a dual, molecular-mechanical process. From an energetic point of view, a tribocoupling operating under steady-state conditions can be viewed as a stationary thermodynamic system, and the energy conservation law in tribocoupling can be written in the form of the energy balance equation [7]: where , , In turn, according to V.V. Fedorov's ergo dynamic theory of plastic deformation and destruction of solids [1, 7 -9], the change in total internal energy 1 U ∆ and 2 U ∆ can be represented as the sum of two components: in accordance with (6), we obtain the energy balance equations for each element of the tribocoupling in the form of the first law of thermodynamics: The physical meaning of the components of equation (7) is defined by S.V. Fedorov [7]. of various kinds of elementary defects and damage to the microstructure of deformable volumes of the surface layers of both bodies, determining the measure of their strain hardening, damage and destruction. It is this part of the external energy that reflects the true resistance of the deformable volumes of materials of the contact layers to the relative displacement of surfaces. It is accumulatedit is "destroyed" by friction, "being accumulated" in the structure of these volumes in the form of the potential energy of elastic distortions of the crystal lattice.
The second fraction of the friction work is converted into internal energy 1 Q and 2 Q of the vibration, thermal atoms motion of the surface layers of both elements, defining the "thermal effect of friction". A smaller part of this effect is transformed into the energy of thermal motion of atoms of the crystal structure of deformable volumes. It causes softening and release of the latent energy of defects, an increase in the intensity of atomic vibrations and an increase in the temperature of the surface layers in stationary conditions to values of 1 Т const = Most of the thermal effect is dissipated into the environment.
If expressions (7) are solved with respect to the friction coefficient, we obtain the binomial energy balance equations for each element of the tribocoupling: From the standpoint of I.V. Kragelsky's theory of friction [2], the friction force has a dual, molecular-mechanical nature, and the work of the friction force on the contact can be expressed by the sum of the mechanical mech F and molecular mol F components of the total friction force t F : From equation (9) it follows that the total coefficient of friction is the sum of the mechanical and molecular components: mech mol From a comparison of expressions (8) and (10), which determine the friction coefficient from the energy and molecular mechanical positions, respectively, we can estimate the components of the friction coefficient in the form: -a mechanical component The mechanical component of the friction coefficient under the conditions (13) can be determined by N.M. Mikhina's method [10] depending on the contact type: where , , g a p α θ -hysteresis loss coefficient, the material elastic constant of the element being worn, nominal pressure on the contact, respectively; , a b -constants corresponding to a particular contact type; ∆ -complex parameter of the surface roughness of the counter element, determined from reference data for run-in surfaces [2,10,11].
According to the ergo dynamic theory of the destruction of solids, those local volumes of the surface layer 1 , с ρ -density and heat capacity of triboelements materials. In this case, the volumetric wear of each element of the stationary coupling in the friction path (or during operation time t ) will be: Linear wear of triboelements and coupling in general: 1 2 y y y = + .
Linear wear rate of triboelements and coupling in general: Here 1 2 , Т Т A A -the friction area of the first and second elements of the pair, respectively. Analytical indicators of triboelements wear resistance and coupling in general: 1 1 The expected resource of the tribocoupling is determined by the specified limit value of its linear  Table. Experimental average values of wear resistance of cast iron pads ch И , steel rollers st И and coupling И as a whole in each series of experiments were determined by losing their mass by weighing on the electronic discharge scales IU 215S of the 1st category before and after the tests (see the Table). In tests, the contact temperature was recorded with a CONDTROL IR-T4 infrared thermometer, and the surface roughness of the samples was measured with a Perthometer S2 MAHR instrument before and after the experiment.
The comparison results for all series of experiments were determined by the magnitude of the calculation errors И δ and are presented in the The results of the comparative analysis given in the Table show that the error in predicting the values of wear-resistance of triboelements and coupling in general are in the range: for cast-iron pads -