MODELING AND OPTIMIZATION OF THE PROCESSES OF MOVEMENT AND ACCELERATION OF THE OVERHEAD CRANE TROLLEY IN THE MODE OF DAMPING UNCONTROLLED LOAD OSCILLATIONS
DOI:
https://doi.org/10.31650/2786-6696-2023-4-33-40Keywords:
overhead crane, load trajectory, vibration damping, sway, optimization, movement, acceleration, trolley, rope.Abstract
The paper deals with the modeling and optimization of the processes of movement and acceleration of a bridge crane trolley in the mode of damping uncontrolled oscillations of the load. For the dynamic system of a flat pendulum with vibration damping, which describes the oscillations of a bridge crane load on a flexible rope suspension in a separate vertical plane, it is proposed to use third-order time splines that model the motion and acceleration of the load suspension point in the horizontal direction of the trolley's movement.
To determine the time dependence of the angle of deviation of the crane from the gravitational vertical, it is proposed to use the methods of classical calculus of variations (Euler-Poisson equation), which allow optimizing (minimizing) the value of this angle in the process of accelerating a trolley with a load suspended from the ropes of an overhead crane.
An analytical solution to the problem of damping residual uncontrollable oscillations of the overhead crane load, which usually occur after full acceleration or braking of the load suspension point on the trolley, is obtained. To derive the dependencies, an analytical approach was used to calculate the value of the angle of deviation of the overhead crane's cargo rope from the gravitational vertical, depending on the acceleration and displacement of the load suspension point.
The problem of loosening of a load moved by an overhead crane is considered and solved in a new way that allows to completely avoiding pendulum spatial oscillations of the load on a rope suspension. The mathematical apparatus of linear algebra (Kramer's rule, in particular) is used, which allows us to establish analytically the law of time motion of a rope with a load, the angle of deviation of which from the vertical takes minimum values in the process of acceleration of the cargo trolley.
References
[1] A.V. Shchedrynov, S.A. Serykov, V.V. Kolmykov, "Avtomatycheskaia systema uspokoenyia kolebanyi hruza dlia mostovoho krana", Prybory y systemy. Uravnenye, kontrol, dyahnostyka, no. 8, pp. 13-17, 2007.
[2] O.Y. Tolochko, D.V. Bazhutyn, "Sravnytelnyi analyz metodov hashenyia kolebanyi hruza, podveshennoho k mekhanyzmu postupatelnoho dvyzhenyia mostovoho krana", Elektromashynostroenye y elektrooborudovanye, no. 75, pp. 22-28, 2010.
[3] O.A. Shvedova y dr., "Alhorytmy podavlenyia kolebanyi hruzov podymno-transportnykh mekhanyzmov s yspolzovanyem nechotkoi lohyky funktsyonyrovanyia", Doklady BHUYR, no. 1(79), pp. 65-71, 2014.
[4] F.L. Chernousko, L.D. Akulenko, B.N. Sokolov, Upravlenye kolebanyiamy. M.: Nauka, 980.
[5] A.J. Ridout, "Anti-swing control of the overhead crane using linear feedback", Journal of Electrical and Electronics Engineering, vol.9, no. ½, pp. 17-26, 1989.
[6] H.M. Omar, Control of gantry and tower cranes: PhD Dissertation. Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 2003.
[7] M. Korytov, V. Shcherbakov, E. Volf, "Impact sigmoidal cargo movement paths on the efficiency of bridge cranes", International Journal of Mechanics and Control, vol. 16, no. 2, pp. 3-8, 2015.
[8] V. Shcherbakov, etc., "The reduction of errors of bridge crane loads movements by means of optimization of the spatial trajectory site", Applied Mechanics and Materials, vol. 811, pp. 99-103, 2015.
[9] V. Shcherbakov, etc., "Mathematical modeling of process moving cargo by overhead crane", Applied Mechanics and Materials, vol. 701-702, pp. 715-720, 2014.
[10] Y.S. Kim, etc. "A new vision-sensorless anti-sway control system for container cranes", Industry Applications Conference, vol. 1, pp. 262-269, 2003.
[11] D. Blackburn, etc., "Command Shaping for Non-linear Crane Dynamics", Journal of Vibration and Control, no.16, pp. 477-501, 2010.
[12] N. Singer, W. Singhose, W.Seering, "Comparison of filtering methods for reducing residual vibration", European Journal of Control, no. 5, pp. 208-218, 1999.
[13] S.A. Reshmin, F.L. Chernousko, "A time-optimal control synthesis for a nonlinear pendulum", Journal of Computer and Systems Sciences International, vol. 46, no.1, pp. 9-18, 2007.
[14] G.J.L. Almuzara, I. Flugge-Lots, "Minimum time control of a nonlinear system", Journal of Differential Equations, vol. 4, no. 1, pp. 12-39, 1968.
[15] M.S. Korytov, V.S. Shcherbakov, "Yspolzovanye synusoydalnoi funktsyy dlia modelyrovanyia razghona y tormozhenyia hruza mostovoho krana v rezhyme hashenyia kolebanyi", Vestnyk SybADY, vol. 2(54), pp. 22-28, 2017.
[16] M.S. Korыtov, "Peremeshchenye hruzovoi telezhky mostovoho krana v rezhyme podavlenyia neupravliaemykh kolebanyi hruza", Problemy upravlenyia, no. 2, pp. 10-16, 2017.
[17] V.S. Loveikyn, Raschotы optymalnykh rezhymov dvyzhenyia mekhanyzmov stroytelnykh mashyn, K.: UMKVO, 1990.
[18] V.S. Loveikin, Yu.O. Romasevych, Yu.V. Chovniuk, I.O. Kadykalo, Dynamika y optymizatsiia pidiomno-transportnykh mashyn, K.: TsP «Komprint», 2019.
[19] V.S. Loveikin, Yu.V. Chovniuk, M.H. Dikteruk, S.I. Pastushenko, Modeliuvannia dynamiky mekhanizmiv vantazhopidiomnykh mashyn, K.-Mykolaiv: RVV MDAU, 2004.
[20] V.S. Loveikin, Yu.V. Chovniuk, Yu.O. Romasevych, "Zastosuvannia metodiv variatsiinoho chyslennia v zadachakh optymalnoho upravlinnia vantazhopidiomnymy mashynamy silskohospodarskoho pryznachennia", Pidiomno-transportna tekhnika, no. 2, pp. 3-15, 2010.
[21] Y.Y. Blekhman, Vybratsyonnaia mekhanyka, M.: Fyzmatlyt, 1994.
[22] V.S. Shcherbakov, M.S. Korytov, E.O. Volf, "Alhorytm kompensatsyy neupravliaemykh prostranstvennykh kolebanyi hruza y povyshenyia tochnosty traektoryy eho peremeshchenyia hruzopodyemnym kranom", Vestnyk mashynostroenyia, no.3, pp. 16-18, 2015.
[23] E.Y. Butykov, "Neobychnoe povedenye maiatnyka pry synusoydalnom vneshnem vozdeistvyy", Kompiuternye ynstrumenty v obrazovanyy, no. 2, pp. 24-36, 2008.
[24] N.A. Kylchevskyi, Kurs teoretycheskoi mekhaniky, T.1, M.: Nauka, 1972.
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