3_2022_sen_3

Title of the article DEVELOPMENT OF ANTI-LOCK BRAKING SYSTEMS OF MODERN CARS, INCLUDING ELECTRIC VEHICLES AND HYBRID VEHICLES
Authors

BAKHMUTOV Sergey V., D. Sc. in Eng., Prof., Deputy CEO for Science (Research), FSUE “NAMI”, Moscow, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

UMNITSYN Artem A., First Category Design Engineer of the Department “Combined Powerplants” of the Center “Powerplants”, FSUE “NAMI”, Moscow, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICAL ENGINEERING COMPONENTS
Year 2022
Issue 3(60)
Pages 42–51
Type of article RAR
Index UDK 629.3.017.5
DOI https://doi.org/10.46864/1995-0470-2022-3-60-42-51
Abstract The article provides an analytical overview of the development of automotive anti-lock braking systems (ABS). Some historical aspects of the development of automotive ABS are described. Examples of control algorithms for ABS actuators are given, which demonstrate the practical implementation of various control methods. The change of some technical characteristics of ABS and methods of their control is shown. Predictions are given for the development of anti-lock braking systems in the course of improving road transport and the transition from traditional cars with only an internal combustion engine to hybrid cars and electric vehicles. The experience of the FSUE “NAMI” is shown on the creation of ABS with combined actuators. The possibility of using electric drive machines for driving wheels to work as part of ABS actuators is investigated. Algorithms of joint control of friction braking mechanisms and electric machines have been developed. A set of theoretical and experimental studies of combined ABS actuators has been carried out, confirming the possibility of improving the braking characteristics of a car in various road conditions during emergency braking.
Keywords electric vehicle, anti-lock braking system, combined actuator, control algorithms, comparative evaluation of braking properties
  You can access full text version of the article.
Bibliography
  1. Vlasov K.P. Teoriya avtomaticheskogo upravleniya [Theory of automatic control]. Kharkiv, Gumanitarnyy tsentr Publ., 2007. 526 p. (in Russ.).
  2. Mamdani E.H., Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller. International journal of man-machine studies, 1975, vol. 7, iss. 1, pp. 1–13.
  3. Erjavec J. Automotive brakes. Delmar Cengage Learning, 2003. 471 p.
  4. Petrany M. Anti-lock brakes, the first technology to help you avoid a crash, turn 40. 2018. Available at: https://www.roadandtrack. com/car-culture/car-accessories/a22811340/anti-lockbrakes- the-first-technology-to-help-you-avoid-a-crash-turn-40/ (accessed 16 July 2022).
  5. ABS module. Available at: https://www.bosch-mobility-solutions. com/en/solutions/driving-safety/abs-module/ (accessed 16 July 2022).
  6. Choi S., Cho D.-W. Control of wheel slip ratio using sliding mode controller with pulse width modulation. Vehicle system dynamics, 1999, vol. 32, iss. 4–5, pp. 267–284.
  7. Wellstead P.E., Pettit N.B.O.L. Analysis and redesign of an antilock brake system controller. IEE Proceedings – Control theory and applications, 1997, vol. 144, iss. 5, pp. 413–426.
  8. Ryazantsev V.A. Metod sovershenstvovaniya upravleniya antiblokirovochnoy sistemoy avtomobilya pri individualnom regulirovanii tormoznykh mekhanizmov. Diss. kand. tekhn nauk [Method of improving the control of the anti-lock braking system of the car with individual regulation of braking mechanisms. Ph. D. Thesis]. Moscow, 2019. 166 p. (in Russ.).
  9. Drakunov S., Ozguner U., Dix P., Ashrafi B. ABS control using optimum search via sliding modes. Proceedings of 1994 33rd IEEE Conference on decision and control. Lake Buena Vista, 1994, vol. 1, pp. 466–471. DOI: https://doi.org/10.1109/CDC.1994.411013.
  10. Fang Y., Chu L., Shang M., Zhou F., Guo J. Identification and control of split-μ road for antilock braking system. Proc. 2010 2nd International conference on advanced computer control. Shenyang, 2010, pp. 298–301. DOI: https://doi.org/10.1109/ICACC.2010.5486616.
  11. Savitski D., Ivanov V., Augsburg K., Shyrokau B., Wragge-Morley R., Pütz T., Barber P. The new paradigm of an anti-lock braking system for a full electric vehicle: experimental investigation and benchmarking. Proceedings of the institution of mechanical engineers, Part D: Journal of automobile engineering, 2016, vol. 230, iss. 10, pp. 1364–1377. DOI: https://doi.org/10.1177/0954407015608548.
  12. Digital auto report 2019. Available at: https://www.strategyand. pwc.com/gx/en/insights/2019/digital-auto-report.html.
  13. Bera T.K., Bhattacharya K., Samantaray A.K. Bond graph model-based evaluation of a sliding mode controller for a combined regenerative and antilock braking system. Proceedings of the institution of mechanical engineers, Part I: Journal of systems and control engineering, 2011, vol. 225, iss. 7, pp. 918–934. DOI: https://doi.org/10.1177/2041304110394558.
  14. Zhang J.L., Yin C.L., Zhang J.W. Improvement of drivability and fuel economy with a hybrid antiskid braking system in hybrid electric vehicles. International journal of automotive technology, 2010, vol. 11, iss 2, pp. 205–213. DOI: https://doi.org/10.1007/s12239-010-0026-0.
  15. Mi C., Lin H., Zhang Y. Iterative learning control of antilock braking of electric and hybrid vehicles. IEEE transactions on vehicular technology, 2005, vol. 54, iss. 2, pp. 486–494. DOI: https://doi.org/10.1109/TVT.2004.841552.
  16. Umnitsyn A.A., Bakhmutov S.V. Otsenka vypolneniya trebovaniy deystvuyushchikh standartov v voprose effektivnosti antiblokirovochnoy sistemy elektromobilya s podderzhkoy smeshannogo tormozheniya [Evaluation of compliance with the current standards requirements regarding the anti-lock braking system effectiveness of an electric vehicle with mixed braking support]. Trudy NAMI, 2022, no. 2, pp. 51–59. DOI: https://doi.org/10.51187/0135-3152-2022-2-51-59.
  17. Fujimoto H., Saito T., Noguchi T. Motion stabilization control of electric vehicle under snowy conditions based on yaw-moment observer. Proc. the 8th IEEE International workshop on advanced motion control. Kawasaki, 2004, pp. 35–40. DOI: https://doi.org/10.1109/AMC.2004.1297637.
  18. Zhou Y. Control strategy for ABS of EV with independently controlled four in-wheel motors. Proc. 2009 4th IEEE Conference on industrial electronics and applications. Xi’an, 2009, pp. 2471–2476. DOI: https://doi.org/10.1109/ICIEA.2009.5138647.
  19. Lin C.-L., Lin W.-C. ABS control design for two-wheel drive electric vehicles. Proc. Second international conference on mechanic automation and control engineering. Inner Mongolia, 2011, pp. 1011–1014. DOI: https://doi.org/10.1109/MACE.2011.5987104.
  20. Semmler S. Regelung der Fahrzeugbremsdynamik mit kontinuierlich einstellbaren Radbremsen. Ph. D. Thesis. Düsseldorf, 2006.
  21. Umnitsyn A.A., Bakhmutov S.V. Intelligent anti-lock braking system of electric vehicle with the possibility of mixed braking using fuzzy logic. Journal of physics: conference series, 2021, vol. 2061. DOI: https://doi.org/10.1088/1742-6596/2061/1/012101.
  22. State Standard R 41.13-99. Edinoobraznye predpisaniya kasayushchiesya ofitsialnogo utverzhdeniya transportnykh sredstv v otnoshenii tormozheniya [Uniform provisions concerning the approval of vehicles of categories M, N and О with regard to braking]. Moscow, IPK standartov Publ., 2000 (in Russ.).
3_2022_sen_2

Title of the article PREDICTION OF THE DURABILITY OF THE GRAIN HARVESTER REEL SUPPORT BEARING OPERATING UNDER IRREGULAR LOAD UNDER MECHANO-SLIDING FATIGUE
Authors LIS Ivan N., M. Sc. in Eng., Lecturer of Special Disciplines, Lida College of Yanka Kupala State University of Grodno, Lida, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section DYNAMICS, DURABILITY OF VEHICLES AND STRUCTURES
Year 2022
Issue 3(60)
Pages 35–41
Type of article RAR
Index UDK 539.4
DOI https://doi.org/10.46864/1995-0470-2022-3-60-35-41
Abstract The calculation scheme of the reel of the combine harvester “Lida-1300” is given. The operating time of the bearing of reel support for service life of the combine, the frictional loads of the bearing and the bending stresses of the shaft are determined. Loading blocks are formed with increasing, decreasing and arbitrarily changing load. The influence of values of the softening parameters α and hardening parameters β, the duration of the loading stage on the calculated wear value and durability is analyzed. It has been established that for unchanged or insignificantly changing values of the parameters α and β, the calculated wear values coincide at the end of the loading block, regardless of the order of loads (increasing, decreasing or arbitrarily changing) and the duration of the loading stage. While with a significant difference between the parameters α and β, the coincidence of the calculated wear values at the end of the loading block appears only for a short duration of the loading stage (approximately two orders of magnitude less than the estimated lifetime). A comparison of the calculated wear kinetic curves is made under regular and irregular loading with an operating time of 2.0·107 cycles.
Keywords active system, reel support bearing, durability, mechano-sliding fatigue, irregular loading
  You can access full text version of the article.
Bibliography
  1. Bogdanovich A.V. Prognozirovanie predelnykh sostoyaniy silovykh sistem [Prediction of limit states of active systems]. Grodno, Grodnenskiy gosudarstvennyy universitet Publ., 2008. 371 p. (in Russ.).
  2. Lis I.N., Bogdanovich A.V. Prognozirovanie dolgovechnosti silovoy sistemy, rabotayushchey v usloviyakh friktsionno-mekhanicheskoy ustalosti, na primere podshipnika kolenchatogo vala [Prediction of the active system durability operating under mechano-sliding fatigue using the example of a crankshaft bearing]. Aktualnye voprosy mashinovedeniya, 2021, iss. 10, pp. 129–135 (in Russ.).
  3. Petrovets V.R., Dudko N.I., Samsonov V.L. Tekhnologicheskiy protsess, nastroyka, regulirovka i kontrol kachestva raboty zernouborochnykh kombaynov [Technological process, adjustment, regulation and quality control of combine harvesters]. Gorki, Belorusskaya gosudarstvennaya selskokhozyaystvennaya akademiya Publ., 2012. 56 p. (in Russ.).
  4. Dyachenko A.D., Bednarsky V.V., Kolomytsa V.A., Layko D.V. Eksperimentalnye issledovaniya silovogo vozdeystviya na rabochie organy i privody zernouborochnykh kombaynov [Experimental studies of the power impact on working bodies and drives of combine harvesters]. Nauchnyy zhurnal Rossiyskogo NII problem melioratsii, 2016, no. 3(23), pp. 152–165 (in Russ.).
  5. Khodosevich V.I., Radishevskiy G.A., Kuzmitskiy A.V., Stashinskiy R.S., Avlasenko T.V. Opredelenie osnovnykh parametrov nastroyki i proizvoditelnosti zernouborochnogo kombayna [Determination of the main settings and performance parameters of the combine harvester]. Minsk, Belorusskiy gosudarstvenyy agrarno-tekhnichreskiy universitet Publ., 2007. 56 p. (in Russ.).
  6. TU BY 190526813.001-2015. Kaprolon [Caprolon]. Minsk, Belorusskiy gosudarstvenyy institut standartizatsii i sertifikatsii, 2015. 8 p. (in Russ.).
  7. Sosnovskiy L.A. Statisticheskaya mekhanika ustalostnogo razrusheniya [Statistical mechanics of fatigue failure]. Minsk, Nauka i tekhnika Publ., 1987. 287 p. (in Russ.).
  8. Kogaev V.P., Makhutov N.A., Gusenkov A.P. Raschety detaley mashin na prochnost i dolgovechnost [Calculations of machine parts for strength and durability]. Moscow, Mashinostroenie Publ., 1985. 223 p. (in Russ.).
  9. Reshetov D.N. Mashinostroenie. T. 4-1. Detali mashin. Konstruktsionnaya prochnost. Trenie, iznos, smazka [Mechanical engineering. Vol. 4-1. Machine parts. Structural strength. Friction, wear, lubrication]. Moscow, Mashinostroenie Publ., 1995. 863 p. (in Russ.).
  10. Kogaev V.P., Drozdov Yu.N. Prochnost i iznosostoykost detaley mashin [Strength and wear resistance of machine parts]. Moscow, Vysshaya shkola Publ., 1991. 318 p. (in Russ.).
  11. Troshchenko V.T., et al. Soprotivlenie materialov deformirovaniyu i razrusheniyu. Chast 2 [Resistance of materials to deformation and destruction. Part 2]. Kiev, Nauchnaya mysl Publ., 1994. 701 p. (in Russ.).
  12. Sosnovskiy L.A. Osnovy tribofatiki. Tom 2 [Fundamentals of tribo-fatigue. Volume 2]. Gomel, Belorusskiy gosudarstvenyy universitet transporta, 2003. 234 p. (in Russ.).
  13. Sosnovskiy L.A. Tribofatika: isnosoustalostnye povrezhdeniya v problemakh resursa i bezopasnosti [Tribo-fatigue: wear-resistant damages in lifetime and safety problems]. Moscow–Gomel, NPO TRIBOFATIKA” Publ., FTsNTP “Bezopasnost” Publ., 2000. 304 p. (in Russ.).
  14. State Standard 30638-99. Tribofatika. Terminy i opredeleniya [Tribo-fatigue: terms and definitions]. Minsk, Mezhgosudarstvennyy sovet po standartizatsii, metrologii i sertifikatsii Publ., 1999. 24 p. (in Russ.).
  15. Lis I.N., Bogdanovich A.V. Eksperimentalnoe issledovanie zakonomernostey obratnogo effekta metallopolimernoy silovoy sistemy pri friktsionno-mekhanicheskoy ustalosti [Experimental study of the regularities of the reverse effect of a metal-polymer active system under mechano-sliding fatigue]. Trudy 6 Mezhdunarodnogo simpoziuma po tribofatike MSTF 2010 “Tribofatika” [Proc. 6th International symposium on tribo-fatigue ISTF 2010 “Tribo-fatigue”]. Minsk, 2010, part 1, pp. 707–712 (in Russ.).
  16. Anurev V.I. Spravochnik konstruktora-mashinostroitelya. T. 2 [Handbook of a mechanical engineer designer. Vol. 2]. Moscow, Mashinostroenie Publ., 2001. 900 p. (in Russ.).
  17. Troshchenko V.T., Koval Yu.I. Zakonomernosti nakopleniya ustalostnogo povrezhdeniya v stalyakh 45 i 1Kh13 v usloviyakh programmnogo izmeneniya nagruzki [Patterns of accumulation of fatigue damage in steels 45 and 1X13 (1Kh13) under conditions of programmed load change]. Problemy prochnosti, 1973, no. 12, pp. 9–15 (in Russ.).
  18. Troshchenko V.T. Prochnost metallov pri peremennykh nagruzkakh [Strength of metals under variable loads]. Kiev, Nauchnaya mysl Publ., 1978. 176 p. (in Russ.).
  19. Savkin A.N. Raschetno-eksperimentalnye metody otsenki rasseyannykh povrezhdeniy v metalle i detalyakh mashin pri regulyarnoy i neregulyarnoy peremennoy zagruzhennosti. Avtoref. diss. dokt. tekhn. nauk [Computational and experimental methods for assessing scattered damage in metal and machine parts with regular and irregular variable load. Extended Abstract of D. Sc. Thesis]. Saratov, 2008. 40 p. (in Russ.).
3_2022_sen

MECHANICS OF MOBILE MACHINES
Ishin N.N., Goman A.M., Skorokhodov A.S., Shportko V.V., Panovko G.Ya., Shyshko S.A., Karpovich P.G.
Method for assessing the modal parameters of planetary reducers of mining dump trucks motor wheels during their operational vibration diagnostics
24
DYNAMICS, DURABILITY OF VEHICLES AND STRUCTURES
Lis I.N.
Prediction of the durability of the grain harvester reel support bearing operating under irregular load under mechano-sliding fatigue
35
MECHANICAL ENGINEERING COMPONENTS
Bakhmutov S.V., Umnitsyn A.A.
Development of anti-lock braking systems of modern cars, including electric vehicles and hybrid vehicles
42
Zhdanovich Ch.I., Kalinin N.V.
Selection of the range of gear ratios of the mechanical part of the electromechanical power train of the tractor
52
MECHANICAL ENGINEERING MATERIALS AND TECHNOLOGIES
Rudenko S.P, Valko A.L.
Construction of deep contact fatigue curves for surface-hardened gear wheels
61
MECHANICS OF DEFORMED SOLIDS
Leonenko D.V., Markova M.V.
Vibrations of a three-layer circular step plate under periodic impact
68
Verameichyk A.I., Neroda M.V., Kholodar B.G.
Finite element modeling of the problem of stretching a material with zones of altered structure
77
TRIBO-FATIGUE SYSTEMS MECHANICS
Sosnovskiy L.A.
On the choice of modern structural metal material for high-duty mechanical systems. Part 1
85
OUR JUBILEES
Bakhmutov Sergey Vasilevich (on the occasion of his 70th birthday)
97
3_2022_sen_1

Title of the article METHOD FOR ASSESSING THE MODAL PARAMETERS OF PLANETARY REDUCERS OF MINING DUMP TRUCKS MOTOR WHEELS DURING THEIR OPERATIONAL VIBRATION DIAGNOSTICS
Authors

ISHIN Nikolay N., D. Sc. in Eng., Assoc. Prof., Chief of the R&D Center “Mining Machinery”, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

GOMAN Arkadiy M., Ph. D. in Eng., Assoc. Prof., Head of the Department of Dynamic Analysis and Vibration-based Diagnostics of Machines, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

SKOROKHODOV Andrey S., Ph. D. in Eng., Leading Researcher of the Department of Dynamic Analysis and Vibration-based Diagnostics of Machines, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

SHPORTKO Vladimir V., Researcher of the Department of Dynamic Analysis and Vibration-based Diagnostics of Machines, Joint Institute of Mechanical Engineering of the NAS of Belarus, Minsk, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

PANOVKO Grigory Ya., D. Sc. in Eng., Prof., Chief Researcher, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russian Federation, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

SHYSHKO Sergei A., Deputy Designer General, OJSC “BELAZ” – Management Company of Holding “BELAZ-HOLDING”, Zhodino, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

KARPOVICH Peter G., Head of the Design-Engineering Department, OJSC “BELAZ” – Management Company of Holding “BELAZ-HOLDING”, Zhodino, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICS OF MOBILE MACHINES
Year 2022
Issue 3(60)
Pages 24–34
Type of article RAR
Index UDK 621.833.65:534
DOI https://doi.org/10.46864/1995-0470-2022-3-60-24-34
Abstract Technical condition diagnostics of the planetary reducers of motor wheels in mining dump trucks electromechanical power units requires the study of dynamic processes caused by shock pulses in gearings when tooth remating. The levels of the occurring vibrations are determined by the natural frequencies and natural modes of reducer. The article describes calculation method based on the study of the developed dynamic model of a two-row planetary reducer of a motor wheel, describing the torsional vibrations of its elements and differing from the known ones by taking into account the compound motion of the planetary row satellites, the axes of which rotate together with the carrier. The calculation of natural frequencies and modes of vibrations is reduced to the computation of eigenvalues and eigenvectors of a matrix of special form based on the application of the iterative numerical method of Jacobi rotations. As an example, the calculation is given for gears of the motor wheel reducer of BELAZ mining dump trucks of the 7530 and 7531 series with a load capacity of 220 and 240 tons, respectively. The calculation of the natural frequencies of reducer performed makes it possible to determine those harmonic components of vibration-inducing disturbances in the form of shock pulses which cause resonance phenomena in the mechanism contributing to a significant increase of dynamic loads levels and accelerating the processes of lifetime expense of gear trains. In addition, the analysis of natural modes parameters makes it possible to determine the reducer elements with the highest vibration activity and monitor during vibration monitoring the technical condition of gear trains that limit the reliability of the mechanism.
Keywords mining dump truck, motor wheel reducer, planetary gear train, dynamic model, natural frequencies and modes, technical condition diagnostics
  You can access full text version of the article.
Bibliography
  1. Keuthen M. REXS – standardized gear unit model. Proc. International conference on gears. Garching, Munich, 2019, pp. 701–712. DOI: https://doi.org/10.51202/9783181023556-701.
  2. Algin V.B., Ishin N.N., Starzhinsky V.E., Shil’ko S.V., Rackov M., Čavić M. Development of digital twins for gears and transmissions based on lifetime mechanics and composites mechanics. Aktualnye voprosy mashinovedeniya, 2019, iss. 8, pp. 172–184.
  3. Grib V.V., Zhukov R.V., Perminov M.D., Koltsov V.I., Krasnokutskiy A.N., Efros D.G. Diagnosticheskie modeli izmeneniya tekhnicheskogo sostoyaniya mekhanicheskikh sistem. Chast 2. Vibrodiagnostika. Modalnyy analiz. Konechno-elementnye tekhnologii otsenki tekhnicheskogo sostoyaniya mekhanicheskikh sistem [Diagnostic models of the technical condition change of mechanical systems. Part 2. Vibration diagnostics. Modal analysis. Finite element technologies for assessing the technical condition of mechanical systems]. Moscow, Moskovskiy avtomobilno-dorozhnyy institut (gosudarstvennyy tekhnicheskiy universitet) Publ., 2008. 263 p. (in Russ.).
  4. Kostyukov V.N., Naumenko A.P. Osnovy vibroakusticheskoy diagnostiki i monitoringa mashin [Fundamentals of vibroacoustic diagnostics and monitoring of machines]. Omsk, Omskiy gosudarstvennyy tekhnicheskiy universitet Publ., 2011. 360 p. (in Russ.).
  5. Ayrapetov E.L., Aparkhov V.I., Zhirnov A.A., Kosarev O.I., Chernyavskiy I.T. Analiz vynuzhdennykh parametricheskikh kolebaniy kosozuboy peredachi na AVM [Analysis of forced parametric vibrations of a helical gearing on an analog computer]. Dinamicheskie protsessy v mekhanizmakh s zubchatymi peredachami, 1976, pp. 111–125 (in Russ.).
  6. Ayrapetov E.L., et al. Vibratsii v tekhnike. Tom 3: Kolebaniya mashin, konstruktsiy i ikh elementov [Vibrations in engineering. Volume 3: Vibrations of machines, structures and their elements]. Moscow, Mashinostroenie Publ., 1980. 544 p. (in Russ.).
  7. Berestnev O.V., Goman A.M., Ishin N.N. Analiticheskie metody mekhaniki v dinamike privodov [Analytical methods of mechanics in drives dynamics]. Minsk, Nauka i tekhnika Publ., 1992. 238 p. (in Russ.).
  8. Dinamicheskie protsessy v mekhanizmakh s zubchatymi peredachami [Dynamic processes in mechanisms with gear trains]. Moscow, Nauka Publ., 1976. 155 p. (in Russ.).
  9. Kolebaniya mekhanizmov s zubchatymi peredachami [Vibrations of mechanisms with gear trains]. Moscow, Nauka Publ., 1977. 150 p. (in Russ.).
  10. Parker R.G., Vijayakar S.M., Imajo T. Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons. Journal of sound and vibration, 2000, vol. 237, iss. 3, pp. 435–455. DOI: https://doi.org/10.1006/jsvi.2000.3067.
  11. Kahraman A., Kharazi A.A., Umrani M. A deformable body dynamic analysis of planetary gears with thin rims. Journal of sound and vibration, 2003, vol. 262, iss. 3, pp. 752–768. DOI: https://doi.org/10.1016/S0022-460X(03)00122-6.
  12. Kahraman A., Ding N. A methodology to predict surface wear of planetary gears under dynamic conditions. Mechanics based design of structures and machines, 2010, vol. 38, iss. 4, pp. 493–515. DOI: https://doi.org/10.1080/15397734.2010.501312.
  13. Kalinin D.V. Nelineynye kolebaniya v planetarnykh reduktorakh s podatlivymi oporami tsentralnykh koles [Nonlinear vibrations in planetary reducers with compliant central wheels supports]. Science & education, 2016, no. 10, pp. 69–84. Available at: http://engineering-science.ru/doc/848171.html (accessed 14 September 2021) (in Russ.).
  14. Kalinin D.V., Temis Yu.M. Dinamicheskaya model planetarnogo reduktora turboreaktivnykh dvukhkonturnykh dvigateley [Dynamic model of the planetary reducer of turbojet two-circuit engines]. BMSTU journal of mechanical engineering, 2017, no. 3, pp. 66–75. DOI: https://doi.org/10.18698/0536-1044-2017-3-66-75 (in Russ.).
  15. Mikhaylov V.V., Ishin N.N., Dyko G.A., Gavrilov S.A., Trukhnov L.I. Modelirovanie dinamicheskikh protsessov v planetarnykh reduktorakh motor-koles karernogo samosvala pri troganii i razgone [Simulation of dynamic processes in planetary reducers of a mining dump truck motor wheels during starting and accelerating]. Science & education, 2012, no. 4, pp. 64–68 (in Russ.).
  16. Kostyukov V.N. Obobshchennaya diagnosticheskaya model vibroakusticheskogo signala obektov periodicheskogo deystviya [Generalized diagnostic model of vibroacoustic signal of objects with periodic action]. Omsk scientific bulletin, 1999, iss. 6, pp. 37–41 (in Russ.).
  17. Ognjanović M., Fathi A. Gear vibrations in supercritical mesh-frequency range caused by teeth impacts. Strojniški vestnik, 2010, vol. 56, iss. 10, pp. 653–662.
  18. Yang J., Yang P. Random vibration analysis of planetary gear trains. Journal of vibration and acoustics, 2013, vol. 135, iss. 2. DOI: https://doi.org/10.1115/1.4023053.
  19. Machnev A.V., Machnev V.A., Komarov V.A., Zyabirov I.M. Vibratsionnye protsessy pri rabote korobok peredach traktorov [Vibration processes during operation of tractors gearboxes]. Niva Povolzhya, 2014, no. 4(33), pp. 91–94 (in Russ.).
  20. Ishin N.N. Dinamika i vibromonitoring zubchatykh peredach [Dynamics and vibration monitoring of gear trains]. Minsk, Belorusskaya nauka Publ., 2013. 432 p. (in Russ.).
  21. Kutsubina N.V., Sannikov A.A. Teoriya vibrozashchity i akusticheskoy dinamiki mashin [Theory of vibroprotection and acoustic dynamics of machines]. Ekaterinburg, Uralskiy gosudarstvennyy lesotekhnicheskiy universitet Publ., 2014. 167 p. (in Russ.).
  22. Soami P. Modeling vibration and noise in a gearbox. Available at: https://www.comsol.ru/model/download/903281/models.aco.gearbox_vibration_noise.pdf (accessed 17 September 2021).
  23. Pavlov V.B. Akusticheskaya diagnostika mekhanizmov [Acoustic diagnostics of mechanisms]. Moscow, Mashinostroenie Publ., 1971. 224 p. (in Russ.).
  24. Kechik D.A., Aslamov Yu.P., Davydov I.G., Loshchinin I.V. Otsenka periodichnosti udarnykh impulsov vibratsionnogo signala [Estimation of the periodicity of shock pulses of a vibration signal]. Trudy Respublikanskoy nauchno-prakticheskoy konferentsii “Informatsionnye radiosistemy i radiotekhnologii 2020” [Proc. Republican scientific and practical conference “Information radio systems and radio technologies 2020”]. Minsk, 2020, pp. 229–233 (in Russ.).
  25. Loytsyanskiy L.G., Lure A.I. Kurs teoreticheskoy mekhaniki. Tom 2: Dinamika [Course of theoretical mechanics. Volume 2: Dynamics]. Moscow, Drofa Publ., 2006. 720 p. (in Russ.).
  26. State Standard 16532-70. Peredachi zubchatye tsilindricheskie evolventnye vneshnego zatsepleniya. Raschet geometrii [Cylindrical involute external gear pairs. Calculation of geometry]. Moscow, Standartov Publ., 1983. 43 p. (in Russ.).
  27. State Standard 21354-87 (ST SEV 5744-86). Peredachi zubchatye tsilindricheskie evolventnye vneshnego zatsepleniya. Raschet na prochnost [Cylindrical evolvent gears of external engagement. Strength calculation]. Moscow, Standartov Publ., 1988. 129 p. (in Russ.).
  28. Instruction R.007–2004. Raschet zubchatykh peredach na prochnost [Strength calculation of gears]. Moscow, Rossiyskiy rechnoy reestr Publ., 2004. 91 p. (in Russ.).
  29. Grishkevich A.I., Vavulo V.A., Karpov A.V., Moliboshko L.A., Rukteshel O.S. Avtomobili: Konstruktsiya, konstruirovanie i raschet. Transmissiya [Cars: Construction, design and calculation. Transmission]. Minsk, Vysshaya shkola Publ., 1985. 240 p. (in Russ.).
  30. Andrienko L.A., et al. Detali mashin [Machine elements]. Moscow, Moskovskiy gosudarstvennyy tekhnicheskiy universitet im. N.E. Baumana Publ., 2002. 544 p. (in Russ.).
  31. Artobolevskiy I.I., et al. Vibratsii v tekhnike. Tom 1: Kolebaniya lineynykh sistem [Vibrations in engineering. Volume 1: Vibrations of linear systems]. Moscow, Mashinostroenie Publ., 1978. 352 p. (in Russ.).
  32. Algin V.B., Pavlovskiy V.Ya., Poddubko S.N. Dinamika transmissii avtomobilya i traktora [Car and tractor transmission dynamics]. Minsk, Nauka i tekhnika Publ., 1986. 214 p. (in Russ.).
  33. Algin V.B., Goman A.M., Shportko V.V., Logvinets T.S. Metodika rascheta chastot i form sobstvennykh kolebaniy mekhanicheskikh sistem proizvolnoy struktury so mnozhestvom vozmozhnykh sostoyaniy [Calculation methodology of the natural frequencies and modes of mechanical systems of an arbitrary structure with a plurality of possible states]. Mechanics of machines, mechanisms and materials, 2018, no. 4(45), pp. 36–43 (in Russ.).
  34. Verzhbitskiy V.M. Vychislitelnaya lineynaya algebra [Computational linear algebra]. Moscow, Vysshaya shkola Publ., 2009. 351 p. (in Russ.).