{'fraction_non_alphanumeric': 0.022017220172201722, 'fraction_numerical': 0.005412054120541206, 'mean_word_length': 4.904865649963689, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Evaluation of the degree of abrasive particles activity in oil of machine units involved in the wear process of toothed wheels

This article discusses the regularities of changes in the activity of abrasive particles in the oil of machine units participating in the process of gear-wheel wear at constant and increasing concentrations. They vary depending on the number of loading cycles of gear teeth, considering the share of crushed abrasive particles in one loading cycle of the gear teeth. This makes it possible to obtain regularities in the change of concentrations of active abrasive particles in the oil depending on the gear modules and the number of loading cycles, taking into the account the fraction of crushed abrasive particles per cycle of loading the gear. This technique can be used to determine the duration of the test of the gear wheel material on samples at a constant total concentration of abrasive particles in the oil change for the units of machines with gear drives operating in the presence of abrasive particles in the working environment. The case under consideration corresponds to the operating conditions of the gear transmission in the unit, which allows calculating the oil change period in the units of machines operating in an abrasive environment.


Introduction
One of the factors that most significantly affect the results of calculation and experimental determination of the wear resistance of gear materials is the degree of activity of abrasive particles in the oil of machinery transmission units.
In the process of friction of gear teeth in each cycle of loading, the concentration of active abrasive particles in the oil of the machine constantly changes. It occurs because of crushing abrasive particles, being in oil of the aggregate, and the obtainment of a fresh portion from environment [1,2]. Therefore, when assessing the wear resistance of gear teeth and the oil change period in the units, it is necessary to consider the regularities of activity change of abrasive particles in the process of oil circulation. Analysis of the state of the matter in question showed that in the literature this issue is not sufficiently covered, mainly limited to the study of the process of crushing abrasive particles located in the contact zone of gear teeth [3,4,8,9]. The purpose of this work is to obtain computational dependences for estimating the activity of abrasive particles at their constant and increasing concentrations.

Materials and research methods
In heavily loaded gears, the load falling to the abrasive particles in the wedge-shaped gap of gear teeth in most cases exceeds their compressive strength, as a result of which these particles are subjected to crushing [5,6,10]. Due to the fact that, according to [3,11], the coefficient of re-crushing of abrasive particles is equal to 7 after the crushing process, the size of crushed abrasive particles should not exceed: da<Rz+h0, m, (1) where Rz is the roughness height of the friction surfaces of the gear teeth, m; h0 is the thickness of the oil film between the friction surfaces of the gear teeth, m.
In the process of gear teeth wear, abrasive particles of the size corresponding to expression (1) do not come into force interaction with friction surfaces, and wear from their influence does not occur.
The total concentration of abrasive particles in the oil of the unit can be constant and increasing in time because of their penetration from the environment. Let us see how the abrasive particles activity changes for these cases.

Research results and discussion
The total concentration of abrasive particles in the oil is constant; its value in time remains constant, i.e., no new portions of abrasive particles enter the oil from the outside. This variant is characteristic of testing the roller samples of cogwheels for wear resistance on the friction machine MI-1M. The size of abrasive particles used for wear testing should be greater than the sum of the roughness height and oil film thickness (exceeding 4 microns). In this case, the initial concentration of abrasive particles in the unit oil was taken equal to their total concentration (εmax).
1. During the crushing of active abrasive particles, depending on the number of loading cycles, their concentration decreases ( Figure 1, graphs 1, 2). Let us consider changes of abrasive particles activity in the process of the wear resistance test, after each loading cycle. The loading cycle is one complete revolution of a spherical toothed wheel specimen, which is dipped into oil containing abrasive particles of the spherical shape.
After the first load cycle, the concentration of crushed abrasive particles: where A1 is a coefficient taking into account the share of crushed abrasive particles per cycle of loading at the constant total concentration of abrasive particles in oil. To calculate the A1 value, the dependence is offered [7,12]: where R -radius of the curvature of the sample, surrounded in oil, m; dav -average size of abrasive particles, participating in the wear process, m; 1 -contact length of samples, m; γmoil density, kg/m 3 ; Gm.t -amount of oil, poured into the friction machine tank when testing the wear resistance of samples, made of the cogwheel material, kg. The concentration of active abrasive particles in the friction machine oil after the first loading cycle: . Similarly, after k loading cycles, the concentration of crushed abrasive particles: ( 4) the concentration of active abrasive particles: The obtained analytical dependencies show that at the constant total concentration of abrasive particles, which are in oil, the increase in the abrasive particles size, radius of curvature and the width of contact of samples, made of toothed wheels material, dipped in oils in the friction machine tub, lead to the growth of their crushing intensity. This is explained by the fact that increasing the radius of curvature leads to a narrowing of the wedge-shaped gap between the samples of the friction process. This leads to an increase in the contact area between the surfaces of samples and abrasive particles, due to which, the number of adhered and crushed abrasive particles on the contact surfaces of friction increases.
The received analytical dependences show that at the constant total concentration of the abrasive particles being in oil, the increase in size of abrasive particles, radius of curvature and width of contact of the samples made of the gear wheel material dipped in oils in the bath of friction machine leads to increase in intensity of their crushing. This is explained by the fact that increasing the radius of curvature leads to a narrowing of the wedge-shaped gap between the samples occurring in the friction process, leading to an increase in the contact area between the surfaces of samples and abrasive particles. Thereby this increases the number of adhered and crushed abrasive particles on the contact surfaces of friction.
2. The initial concentration of abrasive particles in the oil of the unit is zero; it increases with increasing the number of loading cycles of the driven gear ( Figure 1, graphs 3, 4). This case corresponds to the real operating conditions of the gear transmission in the unit.
Let us assume that tightness of crankcase and dustiness of environment during exploitation of machines remain constant. As a result, penetrated abrasive particles from the environment are subjected to crushing and the concentration of active abrasive particles in the machine oil changes constantly during each load cycle.
After the first loading cycle of the gear wheel, the concentration of crushed abrasive particles: where n1 -number of gear pairs in the unit, dipping in oil; m -meshing module, m; L -gear tooth length, m; Gm-quantity of oil in the unit, kg; kp -coefficient taking into account the heterogeneity of abrasive particles size that penetrate into the unit, depending on the dusty environment and abrasive particle size value in the oil kp = 0.40 -0.65: Similarly, after k1 cycles of the gear wheel loading, the concentration of crushed abrasive particles: