Copyright © 2019 T.S.Skoblo, A.I. Sidashenko, T.V. Maltsev, V.N.Romanchenko.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Problems of Tribologyy, 24 (3/93) (2019) 6-13 Problems of Tribology Website: http://tribology.khnu.km.ua/index.php/ProbTrib E-mail: tribosenator@gmail.com DOI: https://doi.org/10.31891/2079-1372-2019-93-3-6-13 The use of the optical-mathematical method to describe the structure formation during friction T.S. Skoblo1, A.I. Sidashenko1, T.V. Maltsev2*, V.N.Romanchenko1 1Kharkiv Petro Vasylenko National Technical University of Agriculture, Kharkiv, Ukraine, 2State Enterprise "Malyshev Plant", Kharkiv, Ukraine *E-mail: taras.maltsev@gmail.com Abstract The paper describes the two-periodicity of the compression and tension zones of the serial piston rings surfaces and hardened with a TiN/CrN multilayer ion-plasma coating after bench tests at a sliding speed of 1.3 m/s. The assessment is made from photographs of the microstructure of the surfaces of the rings. The periods of average values of negative, zero, and positive Laplacians were estimated for the columns and rows of photographs. The periods were analyzed by the initial surface and the friction zone, as well as by the general photograph of both ring variants. The result of the evaluation of individual zones revealed a significant difference between the surfaces of the ring with a multilayer ion-plasma coating, both in columns and in rows, which is associated with the wear of the effective coating layer and is confirmed by a decrease in nanohardness. Assessment of the overall photograph revealed a 30 % difference corresponding to a hardened piston ring with nanocoating with the same nature of the compression and tension zones formation, which reflects a sufficiently high resistance to plastic deformation and wear. Key words: multilayer nanocoating, piston ring, friction and wear, nanohardness, optical-mathematical analysis, structure formation, plastic deformation. Introduction The results of previous studies about evaluating the degree and nature of wear of serial oil scraper piston rings of the D100 diesel generator showed their insufficient wear resistance [1]. To increase their wear resistance, the authors studied the possibility of applying a hardening multilayer ion-plasma coating of the TiN/CrN system, which ensured a multiple increase in operational properties at different sliding speeds [2 - 4]. To assess the stress-strain state of various zones of serial rings during friction and hardened by an ion- plasma coating, it became necessary to use the optical-mathematical method for describing structural changes on their working surface [2, 4, 5]. This method allows to identify the relationship between the operating parameters and the formed structure in the contacting surfaces of the products, which can be estimated by approximating their digital images. Also, this method allows to assess the degree of generated stress and identify the zone of their maximum concentration [6 - 10]. After in these studies on the surfaces photographs after testing the piston rings for wear, two-periodicity of the compression and tension regions was revealed [2, 4, 5], it became necessary to describe these zones analytically. The aim of the study is an analytical description of the two-periodicity of the compression and tension zones of the surfaces of serial piston rings and hardened by a TiN/CrN multilayer ion-plasma coating after bench tests at a sliding speed of 1.3 m/s from their electron-microscopic photographs of the friction surface. Research Methodology To carry out the calculations, energy parameters were used and periods of average values of negative, zero, and positive Laplacians were estimated from the columns and rows of photographs of the initial surface Problems of Tribology 7 and the friction zone of serial (Figs. 1, 3) and hardened rings (Figs. 2, 4), respectively. Additionally, we analyzed the general images of the serial and hardened ring variants after the tests, Fig. 5, 6, respectively. The calculation algorithm is implemented as a subroutine. The program itself sends the corresponding values to the subroutine. In each photograph (Fig. 1 - 6), the subroutine searches for the values of the each periods of its pixels in columns and rows. The cycle for trial periods was calculated in the range from 2 to 200 pixels, according to the following source data: qjs – array of average values; 1 js – average fraction of negative Laplacians by columns or rows; 2 js – average fraction of zero Laplacians by columns or rows; 3 js – average fraction of positive Laplacians by columns or rows. Moreover, the indices in the algorithm have the following meaning: q – the number of the sign (1 negative, 2 zero, 3 positive); i – the group number of the same trial period; j – the number inside the same group of the same trial period; t – the trial period in pixels. The number of periods was equal to the integer part of the number of pixels divided by the period. Then, the total algebraic deviation from the average value of the fractions of negative, zero, and positive Laplacians inside the trial period was calculated using formula (1). / 1 t qj j q s a t   . (1) The calculation of the average values of the shares of negative, zero, and positive Laplacians inside the trial period is carried out according to the formula (2).   1 t q qj q j b s a    . (2) After that, it was used the absolute value of the deviation from the average value according to the formula (3). qq bb  . (3) The total value of the functional inside the trial period was found from formula (4), and from it the accumulation of functional according to formula (5). 1 2 3ic b b b   , (4) icff  . (5) Fig. 1. Microstructure of the initial surface of the serial ring Problems of Tribology 8 Fig. 2. Microstructure of the initial surface of the hardened ring Fig. 3. The microstructure of the friction surface of the serial ring at a sliding speed of 1.3 m/s Fig. 4. The microstructure of the friction surface of the hardened ring at a sliding speed of 1.3 m/s Based on the results of the cycle calculation, an array of trial periods functionals was created. The created array was sorted in descending of functionals to detect the most significant changes. Table 1 - 4 presents the calculated periods, where the first column is the period in pixels, and the second is the corresponding functional. As the table 1 - 4 show, the values of the functionals of both ring options differ in the results of counting in columns and in the rows of photographs of the initial and friction surfaces. However, if we compare Problems of Tribology 9 the functionals exclusively in rows or columns, then we can highlight a certain pattern. When counting by columns, the maximum functional of the initial surface of the serial ring is 13.7 % lower than its friction zone (see Tables 1, 3), and the hardened one is 32 % higher (see Tables 2, 4). However, a row calculation shows that the largest functional of the initial surface of a serial ring is 4 % higher than its friction zone (see Tables 1, 3), and hardened - 8.2 % lower, respectively. In both cases, both in columns and in rows, the largest difference between the surfaces is characteristic of a ring with a multilayer ion-plasma coating. Table 1 Values of periods and corresponding functionals of the initial surface photograph of the serial ring By columns By rows period functional period functional 2 0466 2 0883 3 0461 3 0866 154 0456 123 0855 5 0448 4 0813 114 0438 5 0807 59 0433 120 0791 17 0432 139 0779 53 0432 104 0771 158 0430 167 0765 21 0429 173 0764 Table 2 Values of periods and corresponding functionals o f the initial surface photograph of the hardened ring By columns By rows period functional period functional 3 0559 2 0805 172 0514 3 0805 2 0502 127 0763 173 0500 200 0749 176 0497 89 0739 4 0489 157 0738 127 0486 5 0733 132 0483 4 0730 16 0481 18 0717 59 0478 65 0717 Table 3 Values of periods and corresponding functionals of the friction surface photograph of the serial ring By columns By rows period functional period functional 2 0540 3 0848 3 0526 2 0837 176 0508 4 0795 170 0499 152 0752 131 0491 93 0733 166 0474 5 0731 75 0471 95 0725 130 0468 136 0725 12 0467 164 0721 4 0465 33 0718 Problems of Tribology 10 Table 4 Values of periods and corresponding functionals of the friction surface photograph of the hardened ring By columns By rows period functional period functional 3 0380 3 0877 193 0375 2 0831 5 0373 159 0767 94 0365 7 0764 47 0364 6 0760 2 0362 5 0742 177 0362 138 0740 125 0359 4 0728 185 0359 134 0722 178 0355 9 0718 This result, most likely, is associated with the wear of the effective coating layer, which is confirmed by a sharp decrease in the nanohardness of the hardened ring (initial microhardness of TiN/CrN was 53 – 59 GPa) after testing, the level of which approached the - starting material (4 - 4.7 GPa). This is also indicated by the value of the maximum functional of the rings (calculated according to the rows of the friction zones, see Tables 2, 4). Fig. 5. General photo of the initial (left) structure and friction surface (right) of the serial ring Fig. 6. General photo of the initial (left) structure and friction surface (right) of the hardened ring Problems of Tribology 11 So, on average, in columns the maximum functional of a serial ring is lower than the hardened one. The same indicator, that calculated in the rows, lower relative to the hardened ion-plasma multilayer coating of the working layer on average 30 %, which reflects its higher plastic deformation resistance in the considered directions. Moreover, the difference in columns and rows in both ring options is 26 %. This also indicates about the same distribution of compression and tension zones under identical operating conditions. Table 5 Values of periods and corresponding functionals in the general photographof the serial ring after operation By columns By rows period functional period functional 3 1311 2 0969 2 1256 159 0922 5 1152 3 0921 4 1138 5 0881 139 1131 4 0853 89 1122 105 0846 7 1108 6 0832 156 1097 128 0824 13 1093 7 0823 114 1087 115 0820 Table 6 Values of periods and corresponding functionals in the general photograph of the hardened ring after operation By columns By rows period functional period functional 3 1323 3 0973 2 1232 2 0932 4 1177 188 0896 5 1172 4 0867 175 1172 119 0857 182 1166 22 0849 103 1155 87 0848 7 1110 111 0840 116 1109 180 0839 114 1107 135 0835 It is possible that a high spread in the functionalities of individual ring surfaces (see Tables 1 - 4) is directly related to the separation of the general image into individual fragments. Considering that the alternation of compression and tension zones was previously recorded over the entire volume of the material of the ring working surface [5], an additional assessment was made of the functionals calculated values (Tables 5, 6) of the general photograph of both considered options (Fig. 5, 6) after testing, which show a distinctive regularity, both in rows and in columns. Conclusions The studies of the nanostructured state showed the effectiveness of the proposed method for the analytical assessment of the compression and tension zones of the piston rings after friction and wear tests, namely: - the greatest effect is achieved when calculating the functionals, the corresponding periods of the structure variability for the general picture of the working surface and the boundary in the ring; - the revealed pattern during hardening by nanocoating reflects its rather high resistance to plastic deformation and wear; - the difference corresponding to the variant of hardening by nanocoating of the piston ring reaches 30% with the same character of the formation process of compression and tension zones. Problems of Tribology 12 References 1. Скобло Т.С. Особенности изнашивания маслосъемных поршневых колец с покрытием олова при стендовых испытаниях на трение и износ [Текст] / Т. С. Скобло, А. И. Сидашенко, Т. В. 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В роботі виконано опис двухперіодічності зон стиснення і розтягування поверхонь серійних поршневих кілець і, зміцнених багатошаровим іоно-плазмовим покриттям TiN/CrN після стендових випробувань при швидкості ковзання 1,3 м/с. Оцінка виконана по фотографіях мікроструктури поверхонь кілець. Були оцінені періоди середніх значень негативних, нульових і позитивних лапласіанів по стовпцях і рядках фотографій. Аналіз періодів здійснювався по вихідній поверхні і зоні тертя, а також по загальній фотографії обох варіантів кілець. Результат оцінки окремих зон виявив істотну різницю між поверхнями кільця з багатошаровим іонно-плазмовим покриттям, як за стовпцями, так і по рядках, що пов'язано зі зносом ефективного шару покриття і підтверджується зниженням нанотвердості. Оцінка загальної фотографії виявила різницю 30%, що відповідає зміцненому поршневому кільцю нанопокриттям при однаковому характері формування зон стиснення і розтягування, що відображає досить високий опір пластичній деформації і зношуванню. Ключові слова: багатошарове нанопокриття, поршневі кільця, тертя і зношування, нанотвердість, оптико-математичний аналіз, структуроутворення, пластична деформація.