Conformal Efficiency Factors of Friction Pairs in Construction Machinery

. Formulae for the efficiency factor of moving friction pairs of construction equipment are investigated in terms of their mutual adaptation (conformism) during friction and wear. As a basis, the average coefficients of sliding friction and dimensions of the reference line curves, the half-sums of their products of the worn surfaces microrelief for mating parts are taken. Coefficients of sliding friction and dimensions of reference lines were determined from the partial values of microwear and micromaterial of the normalized system of relative reference lines and convergences. Calculated values of conformal efficiency factors were compared with efficiency factors obtained from the tested dependence, as well as from the wedge operator in the dry friction mode. The research was carried out on the example of model hinges of hydraulic excavator attachments.


Introduction
The efficiency factor is the most important tribotechnical characteristic [1][2][3]. There are no approved design dependencies to determine it in respect to friction units of the construction machinery. Recently, the efficiency factor of worn part surfaces coupled by microtopographic indicators has been studied [4][5][6]. In particular, a slight discrepancy between efficiency factors of pins (40 to 41.3 %) and bushings (39.2 to 40.8 %) with average values of about 40% corresponded to the efficiency factor of the classical "wedge operator" has been found [7,8].
Of scientific and applied interest is the comparison of element-wise efficiency factors determined by the microrelief indicators of each mating part with the efficiency factor of the friction pair, taking into account mutual adaptation (conformism) of rubbing elements as a result of friction and wear self-organization.
The purpose of this work is to form analytical formulae for determining the conformal efficiency factor of friction pairs.

The targets are:
1. Constructing normalized systems of relative reference lines and approximations of the microrelief of parts. 2. Determining partial values of microwear and micromaterial.
3. Determining sliding friction coefficients of parts. 4. Determining the relative length of the reference lines curve. 5. Forming analytical formulae for elemental efficiency factors. 6. Forming conformal formulae for the efficiency factors of conjugations. 7. Comparing conformal and elemental efficiency factors. 8. Analysis of research results and formulation of conclusions.

The research methodology
The objects of research are model hinges of borated pins and bushings of hydraulic excavator attachments [9,10]. Normalized systems of relative reference lines (tp) and convergences (ε) were constructed using profilograms of worn surfaces [7] (see Figs. 1 -4).

Normalized systems of relative reference lines (tp) and convergences
The initial microrelief parameters are partial values of microwear, Dа and micromaterial, Dm, determined from the ratios where а m С С is the relative center-to-center distance (bicentroid L E ) of the partial values D а and D ୫ ; а С Р and m С P are approach and addendum components of the bicentroids L E ; Р is the system pole; D а + D ୫ = 1,0.
The sliding friction coefficient of parts is determined by the formula The relative length of the reference lines curve (hypsogram L J ) is estimated by the following dependence Elemental efficiency factors (K) are determined by the formula where pp t is the relative reference line at polar convergence p H (see Figs. 1 -4). Conformal efficiency factors are formed as follows: where 1 2 , f f ; 1 2 , L L are the coefficients of friction and dimensions of the reference line curves of the pins and bushings, respectively.

5,6% '
, which indicates the possibility of practical use of these formulae to assess the efficiency factors of hinge pairs. Close coincidence of the efficiency values calculated by formulae (4), (5), and (6) allows the control of its determination accuracy. At the same time, the newly proposed formulae (5) and (6)  Based on this average value of the coefficient, the efficiency factor is determined by the following dependence: The obtained value is apparently consistent with the above and with the efficiency factor for dry sliding friction, in particular [8].
The dependence (7) is preferable, because the relative dimension of the reference lines curve LJ is not required to determine the efficiency factor. The exponent 0.382 is the typical number of the golden ratio [10] indicating the friction and wear self-organization.
Particular value of the efficiency factor calculated from the given coefficient of sliding friction will indicate the type of friction being realized.
Forecasting of the friction type based on the known coefficient of sliding friction and the efficiency factor calculated from it is shown using the example of rubbing pairs of disc friction safety clutches [11]. Table 2 shows the initial and calculated parameters.  (8) is 73 -84 % that can be considered as mixed boundary-hydrodynamic friction. 3. The comparison of the efficiency factors from items 1 and 2 for lubricated friction, the values obtained by the formula (7) are more consistent with the actual friction conditions. 4. The calculation according to the formula (7) confirms the efficiency factor ranges for dry friction in the range of 37 -52 %, and for lubricated boundary friction in the range of 56 -68 %.

Conclusion
The investigated part-wise and conformal (adaptive) methods for determining efficiency factors are quite satisfactorily consistent with each other in assessing the efficiency factor and typical friction and lubrication modes. The use of various initial parameters of the microrelief of friction surfaces with their close numerical correspondence for determining the efficiency factor may indicate the friction and wear self-organization.