Determination of stiffness and damping characteristics of the adaptive suspension system to develop the optimal control of the simulation bench

Abstract

BACKGROUND: Optimization of the suspension system, its operating parameters, as well as active adjustment depending on the ground surface can significantly affect the fatigue resistance, improve comfort during operation ensuring smoothness of ride, reduce the pressure on ground, increase the overall energy efficiency of the mobile energy unit. Therefore, in this approach, there are theoretical calculations to find the optimal range for control of the simulation bench to study the parameters of the active suspension system.

AIM: Development of optimal operating conditions of the control system of the simulation bench, minimization of vibrations and oscillations, prediction of the system behavior in different conditions and modes of operation.

METHODS: The development of optimal control is based on the analysis of scientific works, including publications, scientific papers and other sources of information on the approaches to the development of optimal control of the performing device in the active suspension system for the most effective damping of vibrations arising from road unevenness. The method of theoretical calculation of three-factor experiment was used, the main dependencies were obtained.

RESULTS: The obtained equations have a high level of significance. Graphical representation makes it possible to make a qualitative assessment of the accuracy of the obtained equations. The equations make it possible to control the parameters of the adaptive suspension system with several criteria. Each criterion included in the equation influences on the function itself. In order to develop the optimal control, the obtained equations are applied in the software development.

CONCLUSION: The practical significance lies in the developed equations for the software concerning the optimal control of the simulation bench, the relationship between independent variables such as velocity, microprofile height and suspension stiffness has been established.

Keywords

adaptive system / pneumatic element / stiffness / dynamics / mobile energy unit / mathematical model / sprung and unsprung masses / oscillations / road surface profile

References

[1] Fomin AB, Zheglov LF. Matematicheskaya model dvizheniya polnoprivodnoy kolesnoy ma-shiny po doroge s tverdoy nerovnoy poverkhnostyu. Nauka i obrazovanie. MGTU im. N.E. Baumana. 2013;11. (In Russ). doi: 10.7463/1113.0645575

[2] Фомин А.Б., Жеглов Л.Ф. Математическая модель движения полноприводной колёсной машины по дороге с твёрдой неровной поверхностью // Наука и образование. МГТУ им. Н.Э. Баумана. 2013. № 11. doi: 10.7463/1113.0645575

[3] Polungyan AA, Fominykh AB. Matematicheskaya model dinamiki transmissii kolesnoy mashiny pri dvizhenii po tverdoy nerovnoy doroge. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie. 2003;4:15–25. (In Russ).

[4] Полунгян А.А., Фоминых А.Б. Математическая модель динамики трансмиссии колёсной машины при движении по твёрдой неровной дороге // Вестник МГТУ им. Н.Э. Баумана. Сер. Машиностроение. 2003. № 4. С. 15–25.

[5] Zhileykin MM. Matematicheskaya model pryamolineynogo dvizheniya kolesnoy mashiny s ba-lansirnoy podveskoy mostov po nerovnostyam puti. Transportnoe i energeticheskoe mashinostroenie. 2016;1:43–49. (In Russ). doi: 10.18698/0536-1044-2016-1-43-49

[6] Жилейкин М.М. Математическая модель прямолинейного движения колёсной машины с балансирной подвеской мостов по неровностям пути // Транспортное и энергетическое машиностроение. 2016. № 1. C. 43–49. doi: 10.18698/0536-1044-2016-1-43-49

[7] Pobedin AV, Dolotov AA, Shekhovtsov VV. Decrease of the Vibration Load Level on the Tractor Operator Working Place by Means of Using of Vibrations Dynamic Dampers in the Cabin Suspension. Procedia Engineering. 2016;150:1252–1257. doi: 10.1016/j.proeng.2016.07.136

[8] Pobedin A.V., Dolotov A.A., Shekhovtsov V.V. Decrease of the Vibration Load Level on the Tractor Operator Working Place by Means of Using of Vibrations Dynamic Dampers in the Cabin Suspension // Procedia Engineering. 2016. Vol. 150. P. 1252–1257. doi: 10.1016/j.proeng.2016.07.136

[9] Mohammadikia R, Aliasghary M. Design of an interval type-2 fractional order fuzzy controller for a tractor active suspension system. Computers and Electronics in Agriculture. 2019;167:105049. doi: 10.1016/j.compag.2019.105049

[10] Mohammadikia R., Aliasghary M. Design of an interval type-2 fractional order fuzzy controller for a tractor active suspension system // Computers and Electronics in Agriculture. 2019. Vol. 167. P. 105049. doi: 10.1016/j.compag.2019.105049

[11] Ramon H, De Baerdemaeker J. A modelling procedure for linearized motions of tree structured multibodies-2: Design of an active spray boom suspension on a spraying-machine. Computers & Structures. 1996;59(2):361–375. doi: 10.1016/0045-7949(95)00247-2

[12] Ramon H., De Baerdemaeker J. A modelling procedure for linearized motions of tree structured multibodies-2: Design of an active spray boom suspension on a spraying-machine // Computers & Structures. 1996. Vol. 59, N. 2. P. 361–375. doi: 10.1016/0045-7949(95)00247-2

[13] Shen-Lung Tung, Yau-Tarng Juang, Wei-Hsun Lee, et al. Optimization of the exponential stabilization problem in active suspension system using PSO. Expert Systems with Applications. 2011;38(11):14044–14051. doi: 10.1016/j.eswa.2011.04.212

[14] Shen-Lung Tung, Yau-Tarng Juang, Wei-Hsun Lee, et al. Optimization of the exponential stabilization problem in active suspension system using PSO // Expert Systems with Applications. 2011. Vol. 38, N. 11. P. 14044–14051. doi: 10.1016/j.eswa.2011.04.212

[15] Kazakova EM. Kratkiy obzor metodov optimizatsii na osnove roya chastits. Vestnik KRAUNTs. Fiz.-mat. nauki. 2022;39(2):150–174. (In Russ). doi: 10.26117/2079-6641-2022-39-2-150-174

[16] Казакова Е.М. Краткий обзор методов оптимизации на основе роя частиц // Вестник КРАУНЦ. Физ.-мат. науки. 2022. Т. 39, № 2. C. 150–174. doi: 10.26117/2079-6641-2022-39-2-150-174

[17] Cleghorn CW, Engelbrecht AP. Particle swarm convergence: an empirical investigation. In: 2014 IEEE Congress on Evolut. Comput. (CEC). IEEE, 2014:2524–2530. doi: 10.1007/978-3-319-09952-112

[18] Cleghorn C.W., Engelbrecht A.P. Particle swarm convergence: an empirical investigation. In: 2014 IEEE Congress on Evolut. Comput. (CEC). IEEE, 2014. P. 2524–2530. doi: 10.1007/978-3-319-09952-112

[19] Zhileykin MM, Fedotov IV. Algoritm kompleksnogo optimalnogo upravleniya dempfirovaniem v podveske kolesnykh mashin. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie. 2017;8:46–53. (In Russ). doi: 10.18698/0536-1044-2017-8-46-53

[20] Жилейкин М.М., Федотов И.В. Алгоритм комплексного оптимального управления демпфированием в подвеске колёсных машин // Известия высших учебных заведений. Машиностроение. 2017. № 8. C. 46–53. doi: 10.18698/0536-1044-2017-8-46-53

[21] Lovchakov VI, Sukhinin BV, Surkov VV. Optimalnoe upravlenie elektrotekhnicheskimi obektami. Tula: TulGU; 2005. (In Russ).

[22] Ловчаков В.И., Сухинин Б.В., Сурков В.В. Оптимальное управление электротехническими объектами. Тула: ТулГУ, 2005.

[23] Ivaykin V. Ispolzovanie skolzyashchikh rezhimov v regulirovanii. Sovremennye tekhnolo-gii avtomatizatsii. 2006;1:90–94. (In Russ).

[24] Ивайкин В. Использование скользящих режимов в регулировании // Современные технологии автоматизации. 2006. № 1. C. 90–94.

[25] Sukhorukov AV. Upravlenie dempfiruyushchimi elementami v sisteme podressorivaniya bystrokhodnoy gusenichnoy mashiny. [dissertation] Moscow; 2003. (In Russ).

[26] Сухоруков А.В. Управление демпфирующими элементами в системе подрессоривания быстроходной гусеничной машины. дисc. ... канд. техн. наук. Москва, 2003.

[27] Zhileykin MM, Kalinin PS, Fedotov IV. Sintez aktivnoy dinamicheskoy nepreryvnoy sistemy upravleniya podveskoy mnogoosnogo kolesnogo shassi. Trudy NAMI. 2012;249:60–86. (In Russ). EDN: OZMDKF

[28] Жилейкин М.М., Калинин П.С., Федотов И.В. Синтез активной динамической непрерывной системы управления подвеской многоосного колёсного шасси // Труды НАМИ. 2012. № 249. С. 60–86. EDN: OZMDKF

[29] Alekseev AA. Vybor zakona upravleniya adaptivnoy sistemoy podressorivaniya avtomobilya. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie. 2007;4:21–25. (In Russ). EDN: TZVPNV

[30] Алексеев А.А. Выбор закона управления адаптивной системой подрессоривания автомобиля // Известия высших учебных заведений. Машиностроение. 2007. № 4. С. 21–25. EDN: TZVPNV

[31] Oleynikov AS. Razrabotka kvazioptimalnogo diskretnogo upravleniya zhestkostyu vibro-zashchitnoy sistemy: [dissertation] Volgograd; 2014. (In Russ). EDN: ZPLKEJ

[32] Олейников А.С. Разработка квазиоптимального дискретного управления жёсткостью виброзащитной системы: дисc. ... канд. техн. наук. Волгоград, 2014. EDN: ZPLKEJ

[33] Godzhaev Z, Senkevich S, Malakhov I, Uyutov S. Development of a mathematical model of the oscillatory system of agricultural mobile power equipment with attachments for the creation of their adaptive springing systems. E3S Web of Conferences. 2023;413:02042. (In Russ). EDN: YZMVZT doi: 10.1051/e3sconf/202341302042

[34] Godzhaev Z., Senkevich S., Malakhov I., Uyutov S. Development of a mathematical model of the oscillatory system of agricultural mobile power equipment with attachments for the creation of their adaptive springing systems // E3S Web of Conferences. 2023. Vol. 413. P. 02042. EDN: YZMVZT doi: 10.1051/e3sconf/202341302042

[35] Godzhaev Z, Senkevich S, Uyutov S, et al. Substantiation of the range of changes in the elastic-damping and inertial characteristics of the oscillatory system of agricultural MES with mounted technological equipment. BIO Web of Conferences. 2024;84:05045. (In Russ). EDN: HNLMOB doi: 10.1051/bioconf/20248405045

[36] Godzhaev Z., Senkevich S., Uyutov S., et al. Substantiation of the range of changes in the elastic-damping and inertial characteristics of the oscillatory system of agricultural MES with mounted technological equipment // BIO Web of Conferences. 2024. Vol. 84. P. 05045. EDN: HNLMOB doi: 10.1051/bioconf/20248405045

[37] Godzhaev ZA, Senkevich SE, Malakhov IS, et al. Issledovanie dinamicheskikh kharakteri-stik selskokhozyaystvennykh mobilnykh energosredstv s adaptivnoy khodovoy sistemoy. In.: XVI Vserossiyskaya multi konferentsiya po problemam upravleniya (MKPU-2023) : materialy multi konferentsii. V 4 t., Volgograd, 11–15 sentyabrya 2023 goda. Volgograd: VolgGTU; 2023;4:48–50. (In Russ). EDN: KQRVIT

[38] Годжаев З.А., Сенькевич С.Е., Малахов И.С. и др. Исследование динамических характеристик сельскохозяйственных мобильных энергосредств с адаптивной ходовой системой. В кн.: XVI Всероссийская мульти конференция по проблемам управления (МКПУ-2023) : материалы мульти конференции. В 4 т., Волгоград, 11–15 сентября 2023 года. Т. 4. Волгоград: ВолгГТУ, 2023. С. 48–50. EDN: KQRVIT

[39] Barskiy IB, Anilovich VYa, Kutkov GM. Dinamika traktora. Moscow: Mashinostroenie; 1973. (In Russ).

[40] Барский И.Б., Анилович В.Я., Кутьков Г.М. Динамика трактора. М.: Машиностроение. 1973.

[41] Khachaturov AA. Dinamika sistemy doroga — shina — avtomobil — voditel. Moscow: Mashinostroenie; 1976. (In Russ).

[42] Хачатуров А.А. Динамика системы дорога — шина — автомобиль – водитель. М.: Машиностроение, 1976.

[43] Spiridonov AA. Planirovanie eksperimenta pri issledovanii tekhnologicheskikh protsessov. Moscow: Mashinostroenie; 1981. (In Russ).

[44] Спиридонов А.А. Планирование эксперимента при исследовании технологических процессов М.: Машиностроение, 1981.

Funding

Российский научный фондRussian Science Foundation(№ 23-29-00289)

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