Mathematical model of the dynamics varying the radius jib system loader crane at adjustment movement arm and telescopic section

V. Loveikin Національний університет біоресурсів і природокористування України https://orcid.org/0000-0003-4259-3900
Yu. Romasevich Національний університет біоресурсів і природокористування України https://orcid.org/0000-0001-5069-5929
O. Spodoba Національний університет біоресурсів і природокористування України

Keywords: mathematical model, varying the radius, combination of movements, loader crane, Lagrange equations of the second kind, dynamic loads, load oscillations

Abstract

DOI: https://doi.org/10.32820/2079-1747-2019-24-40-51

In the paper considers the method of constructing a mathematical model in the plane of change of departure of the jib system of a link loader crane with a load. The mathematical model is built with three simultaneous movements, namely, the simultaneous angular movement of the arm, the linear movement of the telescopic section and the oscillatory movement of the gripping device with a load. The functions of changing the kinematic and dynamic characteristics of the jib system while simultaneously moving its links are calculated. The construction of a mathematical model is performed using the Lagrange equations of the second kind. In this case, for the generalized coordinates of the model of a loader crane, the angular coordinates of the position of the links of the jib system and the angular deviation of the load, and the position of the telescopic section is determined by the linear generalized coordinate of the extension of the rod of the drive hydraulic cylinder.

The mechanical characteristics of the drive, presented in the form of quadratic dependencies between the acting forces and the speeds of movement of the rods of the power hydraulic cylinders. The control of the drive elements is represented as equations of the working fluid flow rate with a change in the flow area of the according to a linear law.

As a result, the equation of motion of the loader crane was obtained, taking into account the influence of the inertial component of each link of the jib system and the influence of the oscillatory movement of the load on the dynamic loads of the metal construction and the hydraulic drive elements. The developed mathematical model makes it possible to theoretically determine the effect of the simultaneous movement of the jib and arm on the oscillations of the load, and the effect of the oscillation of the load on the dynamic loads arising in the jib system and elements of the loader crane drive.

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References

Kovalskij, VF 2016, ‘Matematicheskoe modelirovanie dinamiki manipuljacionnoj sistemy mobilnoj transportno-tehnologicheskoj mashiny s uchetom uprugosti zvenev’, Izvestija Moskovskogo gosudarstvennogo tehnicheskogo universiteta MAMI, no. 3, pp. 9-15.

Milto, AA 2016, ‘Dinamicheskij i prochnostnoj analiz gidravlicheskih krano-manipuljatornyh ustanovok mobilnyh transportno-tehnologicheskih mashin’, Kand.teсh.n. thesis, Moskovskiy avtomobilno-dorozhnyiy gosudarstvennyiy tehnicheskiy universitet, Moskva.

Bakaj, BYa 2011, ‘Poperednie predstavlennia rivniannia dynamiky manipuliatora metodom Lahranzha-Eilera’, Naukovyi visnyk NLTU Ukrainy, no. 21.18, pp. 322-327.

Zabolotnyj, KS, Sirchenko, AA & Zhupiev, AL 2016, ‘Ispolzovanie prjamoj zadachi dinamiki dlja rascheta manipuljatora tonnelnogo ukladchika’, Vibratsii v tekhnitsi ta tekhnolohiiakh. Natsionalnyi hirnychyi universytet, no. 2(82), pp. 22-27.

Tertychnyj-Dauri, VJu 2012, Dinamika robototehnicheskih sistem, Nacionalnyj issledovatelskij universitet informacionnyh tehnologij, mehaniki i optiki, Sankt-Peterburg.

Dobrachev, AA, Raevskaya, LT & Shvets, AV 2010, ‘Simulating the dynamic reaction of manipulator supports’, Russian Engineering Research, no. 1, pp. 11-16.

Dobrachev, AA, Raevskaja, LT & Shvec, AV 2014, Kinematicheskie shemy, struktury i raschet parametrov lesopromyshlennyh manipuljatornyh mashin, Uralskij gosudarstvennyj lesotehnicheskij universitet, Ekaterinburg.

Loveikіn, VS & Mіshchuk, DO 2006, ‘Matematychna model dynamiky zminy vylotu krana manipuliatora z zhorstkymy lankamy’, Tekhnika budivnytstva, no.19, pp. 26-29.

Loveikіn, VS & Mіshchuk, DO 2012, ‘Matematychne modeliuvannia zminy vylotu vantazhu manipuliatorom z hidropryvodom’, Hirnychi, budivelni, dorozhni i melioratyvni mashyny, Kyiv, no. 79, pp. 9-15.

Lagerev, IA 2016, Modelirovanie rabochih processov manipuljacionnyh sistem mobilnyh mnogocelevyh transportno-tehnologicheskih mashin i kompleksov, Redakcionno-izdatelskij otdel Brjanskogo gosudarstvennogo universiteta, Brjansk.

Loveikіn, VS & Mіshchuk, DO 2011, ‘Eksperymentalne doslidzhennia dynamiky rukhu shtoka hidrotsylindra pidiomu sharnirnozchlenovanoi strilovoi systemy krana-manipuliatora z hidropryvodom’, Hirnychi, budivelni, dorozhni i melioratyvni mashyny, no. 78, pp. 28-34.

Emtyl, ZK, Bartenev, IM & Tatarenko, AP 2000, ‘O vlijanii podatlivosti rabochej zhidkosti i jelementov gidroprivoda na dinamicheskuju nagruzhennost gidromanipuljatora pri sovmeshhenii dvizhenij zvenev’, Trudy Fizicheskogo Obshhestva Respubliki Adygeja, Izdatelstvo Adygejskogo gosudarstvennogo universiteta, Majkop, no. 6, pp. 83-87.

Emtyl, ZK, Bartenev, IM, Draplyuk, MV, Popikov, P, Buhtoyarov, A & Tatarenko, L 2011, Gidromanipuljatory i lesotehnicheskoe oborudovanie, Nauka, Moskva.

Mіshchuk, DO 2016, ‘Doslidzhennia dynamichnoi modeli hidravlichnoho tsylindra obiemnoho hidropryvod’, Hirnychi, budivelni, dorozhni ta melioratyvni mashyny, Kyiv, no. 87, pp. 74-81.

Lovejkin, VS & Mishchuk, DO 2019, ‘Sintez optimalnogo dinamicheskogo rezhima dvizhenija strely manipuljatora, ustanovlennogo na uprugom osnovanii’, Nauka i tehnika, vol. 18, no. 1, pp. 55-61.